GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 10 Dec 2019, 08:24

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The line represented by the equation y = 4 – 2x is the perpendicular

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 18 Feb 2012, 18:55
7
1
46
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

62% (02:26) correct 38% (02:28) wrong based on 817 sessions

HideShow timer Statistics

The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

(A) (–4, 1)
(B) (–2, 2)
(C) (0, 1)
(D) (0, –1)
(E) (2, 0)

How come the answer will be D? This is how I am trying to solve this.

First, rewrite the line y=4-2x as y = -2x+4 The equation is now in the form y = mx+b where m represents the slope and b represents the y-intercept.Thus, the slope of this line is -2. By definition, if a line is the perpendicular bisector of any line, the slope of line which is perpendicular bisector is the negative inverse of the slope of line G. Since we are told that the line y = -2x+4 is the perpendicular bisector of line segment RP, line segment RP
must have a slope of \(\frac{1}{2}\) (which is the negative inverse of slope of line y).
Now we know that the slope of the line containing segment RP is\(\frac{1}{2}\) but we do
not know its y-intercept. We can write the equation of this line as , y = 1/2x+b, where b represents the unknown y-intercept.
To solve for b, we can use the given information that the coordinates of point R
are (4, 1). Since point R is on the line y = 1/2x+b, we can plug 4 in for x and 1 in for y to get b = -1
Therefore, equation of line RP will become y = 1/2x-1
Also , y = -2x +4 (Equation of perpendicular bisector) -----------------(2)

Equating the two we will get x =2 . Putting this value of x in we get y = 0.

So the points should be (2,0) i.e. answer E.

Where I am getting this wrong guys?

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59632
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 18 Feb 2012, 19:12
14
15
The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

A. (–4, 1)
B. (–2, 2)
C. (0, 1)
D. (0, –1)
E. (2, 0)

Again, there is no need of equations to solve this question. Plot the line y = 4 – 2x (just find the x and y intercepts and draw the line through them):
Attachment:
Bisector.png
Bisector.png [ 16 KiB | Viewed 38104 times ]
Now, it's easy to SEE that no blue point can be the mirror reflection of R around the line but (0, -1).

Answer: D.

P.S. Answer cannot possibly be E (2, 0) as this point lies on the line y=4-2x (substitute the values of x and y to see that it's true).
_________________
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 03 Dec 2010
Posts: 21
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 25 Feb 2012, 07:34
17
5
Hello,

This is how I solved the problem. Since the Slope of line is -2, the line perpendicular to it would have SLope as 1/2. So I used R(4,1) and each options to see which one gives Slope as 1/2. Only option D gives me the co ordinates through which the SLope is 1/2. It took me around a minutes time to solve.

Please let me know if I'm correct ?
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59632
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 25 Feb 2012, 09:30
7
5
priyalr wrote:
Hello,

This is how I solved the problem. Since the Slope of line is -2, the line perpendicular to it would have SLope as 1/2. So I used R(4,1) and each options to see which one gives Slope as 1/2. Only option D gives me the co ordinates through which the SLope is 1/2. It took me around a minutes time to solve.

Please let me know if I'm correct ?


That's perfectly valid approach.

Two lines are perpendicular if and only the product of their slopes is -1. The slope of given line is -2, hence the slope of PR must be 1/2 (negative reciprocal of -2): 1/2*(-2)=-1.

Now, the slope of a line (a line segment) passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2-y_1}{x_2-x_1}\).

So, for our case the slope of PR must be \(m=\frac{1}{2}=\frac{1-y_1}{4-x_1}\) and you can substitute x and y coordinates of each point from answer choices to see for which one this equation will hold true. Only coordinates of a point from option D fits.
_________________
Director
Director
User avatar
V
Joined: 27 May 2012
Posts: 945
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 01 Jul 2012, 03:10
1
Bunuel wrote:
priyalr wrote:
Hello,

This is how I solved the problem. Since the Slope of line is -2, the line perpendicular to it would have SLope as 1/2. So I used R(4,1) and each options to see which one gives Slope as 1/2. Only option D gives me the co ordinates through which the SLope is 1/2. It took me around a minutes time to solve.

Please let me know if I'm correct ?


That's perfectly valid approach.

Two lines are perpendicular if and only the product of their slopes is -1. The slope of given line is -2, hence the slope of PR must be 1/2 (negative reciprocal of -2): 1/2*(-2)=-1.

Now, the slope of a line (a line segment) passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2-y_1}{x_2-x_1}\).


So, for our case the slope of PR must be \(m=\frac{1}{2}=\frac{1-y_1}{4-x_1}\) and you can substitute x and y coordinates of each point from answer choices to see for which one this equation will hold true. Only coordinates of a point from option D fits.


let's have a look
Required slope for line PR = m= 1/2 ( using if two lines are perpendicular then their slopes m1 * m2 = -1 )
option D= ( 0,-1)
Option E = ( 2, 0)

so taking (4,1) and ( 0,-1) and finding slope
= -2/-4 = 1/2 which is of course what we are expecting ,

now taking (4,1) and (2,0) and finding slope

= -1/-2 = 1/2

So also E, satisfies the slope method
So what am I missing , it is said that only one option satisfies the equation 1/2 = (1-y1)/( 4-x1)
Taking E( 2,0)
(1-0)/(4-2) = 1/2

and taking D(0,-1)
(1+1)/(4-0)= 2/4= 1/2

so both D and E satisfy the slope condition , am I missing anything ?
_________________
- Stne
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59632
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 01 Jul 2012, 03:37
stne wrote:
Bunuel wrote:
priyalr wrote:
Hello,

This is how I solved the problem. Since the Slope of line is -2, the line perpendicular to it would have SLope as 1/2. So I used R(4,1) and each options to see which one gives Slope as 1/2. Only option D gives me the co ordinates through which the SLope is 1/2. It took me around a minutes time to solve.

Please let me know if I'm correct ?


That's perfectly valid approach.

Two lines are perpendicular if and only the product of their slopes is -1. The slope of given line is -2, hence the slope of PR must be 1/2 (negative reciprocal of -2): 1/2*(-2)=-1.

Now, the slope of a line (a line segment) passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2-y_1}{x_2-x_1}\).


So, for our case the slope of PR must be \(m=\frac{1}{2}=\frac{1-y_1}{4-x_1}\) and you can substitute x and y coordinates of each point from answer choices to see for which one this equation will hold true. Only coordinates of a point from option D fits.


let's have a look
Required slope for line PR = m= 1/2 ( using if two lines are perpendicular then their slopes m1 * m2 = -1 )
option D= ( 0,-1)
Option E = ( 2, 0)

so taking (4,1) and ( 0,-1) and finding slope
= -2/-4 = 1/2 which is of course what we are expecting ,

now taking (4,1) and (2,0) and finding slope

= -1/-2 = 1/2

So also E, satisfies the slope method
So what am I missing , it is said that only one option satisfies the equation 1/2 = (1-y1)/( 4-x1)
Taking E( 2,0)
(1-0)/(4-2) = 1/2

and taking D(0,-1)
(1+1)/(4-0)= 2/4= 1/2

so both D and E satisfy the slope condition , am I missing anything ?


You can rule out (2,0) (option E), since this point is on the line y=4-2x.
_________________
Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 419
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 26 Oct 2012, 06:29
Bunuel Bro, my question still remains : I understand E is on the line but why does E also result in slope of 1/2 . . E should cause the slope to be -2 since it is on the line. . why does it then cause the slope to be 1/2?

just trying to understand the math of slope here.
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59632
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 26 Oct 2012, 06:41
1
sachindia wrote:
Bunuel Bro, my question still remains : I understand E is on the line but why does E also result in slope of 1/2 . . E should cause the slope to be -2 since it is on the line. . why does it then cause the slope to be 1/2?

just trying to understand the math of slope here.


Point (2, 0) is on line segment PR (see diagram in my post above). PR is perpendicular to line y = 4 – 2x, thus ANY two point from line segment PR will give you the slope which is negative reciprocal of the slope of line y = 4 – 2x, i.e. 1/2.
_________________
SVP
SVP
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2478
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 26 Oct 2012, 09:52
4
2
Concrete way is to find the actual co-ordinates.

Slope of RP = 1/2 and by using 4,1 and slope the equation is y=x/2 -1

solve for point of intersection - x,y = 2,0.

now let P has co-ordinates (x,y)

since intersection is mid point.

(x+4)/2 = 2 and (y+1)/2 = 0 thus D
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 419
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 02 Nov 2012, 00:45
Quote:
solve for point of intersection - x,y = 2,0.


How do you get to know the point of intersection is 2,0?

I understood your solution till the previous step in which you found the equation of the line.
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59632
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 02 Nov 2012, 02:07
Sachin9 wrote:
Quote:
solve for point of intersection - x,y = 2,0.


How do you get to know the point of intersection is 2,0?

I understood your solution till the previous step in which you found the equation of the line.


x-intercept is a value of x for y=0 and similarly y-intercept is a value of y for x=0.

To find x-intercept substitute y=0 and find x.
To find y-intercept substitute x=0 and find y.

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
_________________
Intern
Intern
avatar
Joined: 11 Jul 2012
Posts: 39
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 11 Nov 2012, 08:08
Bunuel, do you think these coordinates are not unique.
Any combination (x,y) for point P that satisfies the equation 2-2*y = 4-x will make RP perpendicular to the line y = 4-2x.
Am I correct to assert that?
Brother Karamazov
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59632
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 12 Nov 2012, 10:02
Ousmane wrote:
Bunuel, do you think these coordinates are not unique.
Any combination (x,y) for point P that satisfies the equation 2-2*y = 4-x will make RP perpendicular to the line y = 4-2x.
Am I correct to assert that?
Brother Karamazov


No, that's not correct. Line y = 4 – 2x not only has to be perpendicular of PR but also has to be bisector of PR (line y = 4 -2x cuts PR into two equal parts at 90°). Therefore the coordinates of P are unique.

Hope it's clear.
_________________
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 01 Sep 2017, 11:59
enigma123 wrote:
The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

(A) (–4, 1)
(B) (–2, 2)
(C) (0, 1)
(D) (0, –1)
(E) (2, 0)



If the line y = 4 - 2x is the perpendicular bisector of line segment RP, then it’s perpendicular to RP at the midpoint of RP. Recall that two lines are perpendicular if their slopes are negative reciprocals of each other. Since the line has a slope of -2, the line segment should have a slope of ½. Thus, let’s first determine which answer choice can be point P so that the slope of RP is ½. We’ll use the slope formula: m = (y2 - y1)/(x2 - x1):

A) (-4, 1)

m = (1 - 1)/(4 - (-4)) = 0

Point P can’t be (-4, 1).

B) (-2, 2)

m = (1 - 2)/(4 - (-2)) = -1/6

Point P can’t be (-2, 2).

C) (0, 1)

m = (1 - 1)/(4 - 0) = 0

Point P can’t be (0, 1).

D) (0, -1)

m = (1 - (-1))/(4 - 0) = 2/4 = 1/2

Point P could be (0, -1).

E) (2, 0)

m = (1 - 0)/(4 - 2) = 1/2

Point P could be (2, 0).

We see that point P could be either (0, -1) or (2, 0), since either one will make RP’s slope ½. Next let’s determine the midpoint of RP if P is either (0, -1) or (2, 0). We use the midpoint formula: ((x1 + x2)/2 , (y1 + y2)/2)). Recall that R = (4,1).

If P = (0, -1), then the midpoint of RP = ((4 + 0)/2, (1 + (-1))/2) = (2, 0).

If P = (2, 0), then the midpoint of RP = ((4 + 2)/2, (1 + 0)/2) = (3, 1/2).

Recall that the line y = 4 - 2x has to include the midpoint of RP. In other words, the midpoint of RP is a point on the line, and hence its coordinates will satisfy the equation of the line.

If P = (0, -1) and the midpoint of RP is (2, 0), is 0 = 4 - 2(2)? The answer is yes, since 0 = 0. We can see that choice D is the correct choice. However, let’s also show that choice E is not the correct choice:

If P = (2, 0) and the midpoint of RP is (3, 1/2), is 1/2 = 4 - 2(3)? The answer is no, since 1/2 ≠ -2.

Alternate Solution:

Since the line segment RP is perpendicular to y = 4 - 2x, the line containing RP must have a slope of 1/2, since the slopes of perpendicular lines are negative reciprocals of each other. Then, the line containing the line segment RP must be of the form y = (1/2)x + b, for some real number b. Since this line contains the point R, its equation must be satisfied when we substitute x = 4 and y = 1; therefore 1 = (1/2)(4) + b. Then, 1 = 2 + b, and thus b = -1.

We know the line that contains the line segment RP has an equation y = (1/2)x - 1. Let’s find the common point of this line with y = 4 - 2x. We set (1/2)x - 1 = 4 - 2x and solve for x:

(1/2)x -1 = 4 - 2x

(5/2)x = 5

x = 2

So, the x-coordinate of the common point is 2. We can substitute x = 2 in either equation to find the y-coordinate: y = 4 - 2(2) = 0. So, the common point is (2, 0).

Note that this common point is the midpoint of R and P. Therefore, if we let P = (a, b), we must have:

(a + 4)/2 = 2 and (b + 1)/2 = 0. We find that a = 0 and b = -1. Thus, P = (0, -1).

Answer: D
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59632
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 06 Oct 2019, 10:08
enigma123 wrote:
The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

(A) (–4, 1)
(B) (–2, 2)
(C) (0, 1)
(D) (0, –1)
(E) (2, 0)

How come the answer will be D? This is how I am trying to solve this.

First, rewrite the line y=4-2x as y = -2x+4 The equation is now in the form y = mx+b where m represents the slope and b represents the y-intercept.Thus, the slope of this line is -2. By definition, if a line is the perpendicular bisector of any line, the slope of line which is perpendicular bisector is the negative inverse of the slope of line G. Since we are told that the line y = -2x+4 is the perpendicular bisector of line segment RP, line segment RP
must have a slope of \(\frac{1}{2}\) (which is the negative inverse of slope of line y).
Now we know that the slope of the line containing segment RP is\(\frac{1}{2}\) but we do
not know its y-intercept. We can write the equation of this line as , y = 1/2x+b, where b represents the unknown y-intercept.
To solve for b, we can use the given information that the coordinates of point R
are (4, 1). Since point R is on the line y = 1/2x+b, we can plug 4 in for x and 1 in for y to get b = -1
Therefore, equation of line RP will become y = 1/2x-1
Also , y = -2x +4 (Equation of perpendicular bisector) -----------------(2)

Equating the two we will get x =2 . Putting this value of x in we get y = 0.

So the points should be (2,0) i.e. answer E.

Where I am getting this wrong guys?


Similar question to practice:
http://gmatclub.com/forum/in-the-rectan ... 44774.html
http://gmatclub.com/forum/in-the-xy-coo ... 43502.html
http://gmatclub.com/forum/in-the-rectan ... 32646.html
http://gmatclub.com/forum/in-the-rectan ... 88473.html
http://gmatclub.com/forum/in-the-rectan ... 29932.html
_________________
Manager
Manager
avatar
S
Joined: 10 Dec 2017
Posts: 151
Location: India
CAT Tests
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 06 Oct 2019, 11:15
enigma123 wrote:
The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

(A) (–4, 1)
(B) (–2, 2)
(C) (0, 1)
(D) (0, –1)
(E) (2, 0)

How come the answer will be D? This is how I am trying to solve this.

First, rewrite the line y=4-2x as y = -2x+4 The equation is now in the form y = mx+b where m represents the slope and b represents the y-intercept.Thus, the slope of this line is -2. By definition, if a line is the perpendicular bisector of any line, the slope of line which is perpendicular bisector is the negative inverse of the slope of line G. Since we are told that the line y = -2x+4 is the perpendicular bisector of line segment RP, line segment RP
must have a slope of \(\frac{1}{2}\) (which is the negative inverse of slope of line y).
Now we know that the slope of the line containing segment RP is\(\frac{1}{2}\) but we do
not know its y-intercept. We can write the equation of this line as , y = 1/2x+b, where b represents the unknown y-intercept.
To solve for b, we can use the given information that the coordinates of point R
are (4, 1). Since point R is on the line y = 1/2x+b, we can plug 4 in for x and 1 in for y to get b = -1
Therefore, equation of line RP will become y = 1/2x-1
Also , y = -2x +4 (Equation of perpendicular bisector) -----------------(2)

Equating the two we will get x =2 . Putting this value of x in we get y = 0.

So the points should be (2,0) i.e. answer E.

Where I am getting this wrong guys?


Equation of Perpendicular Bisector is
Y=4-2X
Equation of a line perpendicular to this line
Y=1/2X+C
This line passes through (4,1)
1=1/2 *4 +C
C=-1
Equation of line through which perpendicular bisector passes or equation of line RP is
Y=1/2 X-1
Coordinates of point P must pass through this Equation
At X=0, Y=-1
So (0,-1) But (2,0) also satisfies this condition.
If (2,0) is the coordinates of point P
Then Mid point of RP(3,1/2), and this must be pass through the line of perpendicular bisector
i.e
Y=4-2X
at X =3, Y=-2( Not 1/2)
So (2,0) is not the coordinates of point P
D:)
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5466
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: The line represented by the equation y = 4 – 2x is the perpendicular  [#permalink]

Show Tags

New post 09 Oct 2019, 03:18
for eqn y = 4 – 2x
slope= -2
so for line with coordiante (4,1) the slope should be 1/2
since both are perpendicular so m1*m2=-1
we get 1/2 for (4,1) & ( 0,-1) only
IMO D



enigma123 wrote:
The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

(A) (–4, 1)
(B) (–2, 2)
(C) (0, 1)
(D) (0, –1)
(E) (2, 0)

How come the answer will be D? This is how I am trying to solve this.

First, rewrite the line y=4-2x as y = -2x+4 The equation is now in the form y = mx+b where m represents the slope and b represents the y-intercept.Thus, the slope of this line is -2. By definition, if a line is the perpendicular bisector of any line, the slope of line which is perpendicular bisector is the negative inverse of the slope of line G. Since we are told that the line y = -2x+4 is the perpendicular bisector of line segment RP, line segment RP
must have a slope of \(\frac{1}{2}\) (which is the negative inverse of slope of line y).
Now we know that the slope of the line containing segment RP is\(\frac{1}{2}\) but we do
not know its y-intercept. We can write the equation of this line as , y = 1/2x+b, where b represents the unknown y-intercept.
To solve for b, we can use the given information that the coordinates of point R
are (4, 1). Since point R is on the line y = 1/2x+b, we can plug 4 in for x and 1 in for y to get b = -1
Therefore, equation of line RP will become y = 1/2x-1
Also , y = -2x +4 (Equation of perpendicular bisector) -----------------(2)

Equating the two we will get x =2 . Putting this value of x in we get y = 0.

So the points should be (2,0) i.e. answer E.

Where I am getting this wrong guys?
GMAT Club Bot
Re: The line represented by the equation y = 4 – 2x is the perpendicular   [#permalink] 09 Oct 2019, 03:18
Display posts from previous: Sort by

The line represented by the equation y = 4 – 2x is the perpendicular

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne