Last visit was: 21 Apr 2026, 18:58 It is currently 21 Apr 2026, 18:58
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Evo23
User avatar
Joined: 18 Jan 2020
Last visit: 26 Aug 2021
Posts: 74
Own Kudos:
180
 [5]
Given Kudos: 269
Posts: 74
Kudos: 180
 [5]
What are the coordinates of the foot of the perpendicular from the 02 May 2020, 06:00
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

63% (02:16) correct 37% (01:54) wrong based on 107 sessions

History

Date
Time
Result
Not Attempted Yet
What are the coordinates of the foot of the perpendicular from the point (2,2) to the line y - 2x - 8 =0?

A. (4,-2)
B. (-4,2)
C. (2,4)
D. (2,-4)
E. (-2,4)
ShowHide Answer
Official Answer
E
avatar
abannore
avatar
Current Student
Joined: 10 Jun 2018
Last visit: 12 Apr 2022
Posts: 47
Own Kudos:
102
Given Kudos: 36
Location: India
Schools: Kenan-Flagler '24 (WL) Jones (A)
GMAT 1: 690 Q49 V34
Schools: Kenan-Flagler '24 (WL) Jones (A)
GMAT 1: 690 Q49 V34
Posts: 47
Kudos: 102
What are the coordinates of the foot of the perpendicular from the 02 May 2020, 07:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
y-2x-8=0
y=2x+8
Slope of this line= 2

Line containing point (2,2) is perpendicular to this line. So product of slopes of both these lines will be -1.
Slope of line perpendicular to y-2x-8=0 is -1/2
Point (2,2) lies on this perpendicular line.
So equation of new line,
y-2=(-1/2)(x-2)
2y-4=-x+2
2y=-x+6

Only (-2,4) satisfies this equation.
Answer E

Posted from my mobile device
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 21 Apr 2026
Posts: 1,921
Own Kudos:
6,854
 [1]
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,921
Kudos: 6,854
 [1]
What are the coordinates of the foot of the perpendicular from the 02 May 2020, 11:23
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
y-2x-8=0
y =2x+8 (Slope intercept form)
The slope of this line= 2

The foot of the perpendicular and the point (2,2) will make a line perpendicular to the given line.
Hence the slope shall be -1/2 ( the product of slope of perpendicular lines = -1)
A. (4,-2) & (2,2): Slope = (2+2)/(2-4)= -2
B. (-4,2) & (2,2): Slope = (2-2)/(2+4) =0
C. (2,4) & (2,2): Slope = =(2-4)/(2-2) = Not defined
D. (2,-4) & (2,2): Slope = (2+4)/(2-2) = Not defined
E. (-2,4) & (2,2): Slope = (2-4)/(2+2)= -1/2

Hence E is the right answer

  • when x coordinate is same for two points, the line is Vertical and the slope is NOT defined
  • when y coordinate is same for two points, the line is horizontal and slope = 0

Evo23
What are the coordinates of the foot of the perpendicular from the point (2,2) to the line y - 2x - 8 =0?
A. (4,-2)
B. (-4,2)
C. (2,4)
D. (2,-4)
E. (-2,4)
Show more
avatar
Avysar
avatar
Joined: 25 Apr 2020
Last visit: 29 Aug 2020
Posts: 42
Own Kudos:
82
Given Kudos: 1
Posts: 42
Kudos: 82
What are the coordinates of the foot of the perpendicular from the 05 May 2020, 07:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The given line is y=2x+8 so the slope of the perpendicular is -1/2
Let us say the equation is y=-(1/2)x+c
Since this line passes through (2,2), let us substitute the values to get c
2=-(1/2)*2+c
So c=3
So the equation of the perpendicular is y=-(1/2)x+3
Since the question asks for the foot of the perpendicular on the given line, it means we need the point that lies on both the line and the perpendicular. At that point the y coordinate has to be the same for both the lines. So let us equate
We get 2x+8=-(1/2)x+3
Solving, (5/2)x=-x=-2
E is the only choice that has -2 as the x coordinate
Hence E

Posted from my mobile device
avatar
Anki1405
avatar
Joined: 15 Nov 2019
Last visit: 15 Sep 2021
Posts: 8
Own Kudos:
13
Given Kudos: 117
Posts: 8
Kudos: 13
What are the coordinates of the foot of the perpendicular from the 15 Sep 2020, 00:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
What are the coordinates of the foot of the perpendicular from the point (2,2) to the line y - 2x - 8 =0?
A. (4,-2)
B. (-4,2)
C. (2,4)
D. (2,-4)
E. (-2,4)
Show more

Foot of perpendicular from point (2,2) must also lie on the given line y-2x-8 =0.

Therefore, When it is put in the above equation must satisfy it.

Given line y = 2x + 8
Putting the given coordinates in the above Line equation, we get

A. -2 = 2x4 + 8 ⇒ -2 = 16 (Does not satisfy) ⇒ Reject
B. 2 = 2x-4 +8 ⇒ 2 = 0 (Does not satisfy)⇒ Reject
C. 4 = 2x2 + 8 ⇒ 4 = 12 (Does not satisfy)⇒ Reject
D.-4 = 2x2 + 8 ⇒ -4 = 12 (Does not satisfy)⇒ Reject
E. 4 = 2x-2 + 8 ⇒ 4 = 4 (Satisfies)- Accepted - Correct answer.
User avatar
Fdambro294
User avatar
Joined: 10 Jul 2019
Last visit: 20 Aug 2025
Posts: 1,331
Own Kudos:
771
Given Kudos: 1,656
Posts: 1,331
Kudos: 771
What are the coordinates of the foot of the perpendicular from the 25 Sep 2020, 00:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Rule 1: the "Foot" of the Perpendicular from Point (2 , 2) to the Line given by y - 2x - 8 = 0 will be the Point at which the Line connected to (2 , 2) will be PERPENDICULAR to the Line given by y - 2x - 8 = 0

Rule 2: the Slop of a Perpendicular Line is the (-)Neg. Reciprocal of the Original Line's Slope


y - 2x - 8 = 0

In Slope Intercept Form:

y = 2x + 8

Slope = m = +2

The (-)Negative Reciprocal of +2 ----- (-)1/2


Thus, the Perpendicular Line must be of the Form: y = (-)1/2x + b

We know that this Line must Intersect Point (2, 2). So we can Plug this Point into the Equation to find the Y-Intercept = b

y = (-)1/2x + b

2 = (-)1/2 * (2) + b

2 = -1 + b

b = 3

The Equation of the Line: y = -1/2x + 3


Finally, we can find the exact Point by setting the 2 Equations Equal and Find the X-Coordinate of their Intersection

y = 2x + 8 = -1/2x + 3 = y

4x + 16 = -1x + 6

5x = -10

x = -2

The Y-Coordinate is given as, after plugging in x = -2:

y = -1/2 * (-2) + 3

y = 4


The Answer is: (X , Y) = (-2 , 4)

-E-
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,957
Own Kudos:
1,117
Posts: 38,957
Kudos: 1,117
What are the coordinates of the foot of the perpendicular from the 06 Mar 2025, 10:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109728 posts
Krunaal
Tuck School Moderator
853 posts