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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

11 Nov 2012, 16:04

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

61% (03:12) correct
39% (02:06) wrong based on 182 sessions

HideShow timer Statistics

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

11 Nov 2012, 17:12

Expert's post

Archit143 wrote:

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC? A. -4/3 B. 2/3 C. 1 D. 4/3 E. 2

I'm happy to help with this.

We know the hypotenuse AC = 5, and we know BC = 3, because B & C have the same y-coordinate (BC is horizontal) and they are separated in the horizontal direction by 3.

If a right triangle has a hypotenuse of 5 and one leg of 3, the other leg has to be 4. That is the inescapable conclusion of the Pythagorean Theorem. We must have a 3-4-5 triangle.

The trouble is ---- we don't know if Z > Y or Z < Y ---- the problem provides no information on that point. Thus, we have a horizontal segment BC of length 3, with a right angle at B, but we don't know whether the perpendicular segment AB goes up or down from B. We know AB must have a length of 4 and that it must make a right angle with B, but we don't know whether the direction from B to A is up or down. Therefore, the slope of AB could be either +4/3 or -4/3. Two answers are possible here.

I suspect either something was not copied correctly from the source, or that the source is faulty.

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

11 Nov 2012, 17:28

mikemcgarry wrote:

Archit143 wrote:

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC? A. -4/3 B. 2/3 C. 1 D. 4/3 E. 2

I'm happy to help with this.

We know the hypotenuse AC = 5, and we know BC = 3, because B & C have the same y-coordinate (BC is horizontal) and they are separated in the horizontal direction by 3.

If a right triangle has a hypotenuse of 5 and one leg of 3, the other leg has to be 4. That is the inescapable conclusion of the Pythagorean Theorem. We must have a 3-4-5 triangle.

The trouble is ---- we don't know if Z > Y or Z < Y ---- the problem provides no information on that point. Thus, we have a horizontal segment BC of length 3, with a right angle at B, but we don't know whether the perpendicular segment AB goes up or down from B. We know AB must have a length of 4 and that it must make a right angle with B, but we don't know whether the direction from B to A is up or down. Therefore, the slope of AB could be either +4/3 or -4/3. Two answers are possible here.

I suspect either something was not copied correctly from the source, or that the source is faulty.

Let me know if you have any questions.

Mike

Hi Mike

First of all thanks for replying to my post.... The actual question is to find the equation of AC which is not difficult after we get the slope.

Pls find below the actual question

In the figure to the left, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the equation of line AC?

The co ordinates remains the same as in the original question.

My doubt is When we get the 3 - 4 -5 triangle with clear value as 3 , 4 and 5 not as ratio, also from the equation we know that change in y axis (delta Y ) is 4 and that of X axis is 3. why cant we conclude straight away that the slope is 4/3 . Yes if we substitute the value of Z as y+ 4 than we get - 4/3

Why is it so.............. The solution assumes the value to be - 4/3 and calculates the equation of line. Question; why is there two possible SLOPE of a single line.........

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

28 Dec 2013, 11:05

Archit143 wrote:

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

A. -4/3 B. 2/3 C. 1 D. 4/3 E. 2

A is the answer to this one

Let me explain

We need to draw the triangle first. Now, x =3 so we are going to have a pythagorean triple 3-4-5. Now are coordinate for A (3,z) C (6,y)

Slope will be (y-z )/ (6-3)

Do we know y-z? Yes we do from the height of the right triangle we get that difference of z-y = 4

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

18 Jan 2014, 21:41

mikemcgarry wrote:

Archit143 wrote:

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC? A. -4/3 B. 2/3 C. 1 D. 4/3 E. 2

I'm happy to help with this.

We know the hypotenuse AC = 5, and we know BC = 3, because B & C have the same y-coordinate (BC is horizontal) and they are separated in the horizontal direction by 3.

If a right triangle has a hypotenuse of 5 and one leg of 3, the other leg has to be 4. That is the inescapable conclusion of the Pythagorean Theorem. We must have a 3-4-5 triangle.

The trouble is ---- we don't know if Z > Y or Z < Y ---- the problem provides no information on that point. Thus, we have a horizontal segment BC of length 3, with a right angle at B, but we don't know whether the perpendicular segment AB goes up or down from B. We know AB must have a length of 4 and that it must make a right angle with B, but we don't know whether the direction from B to A is up or down. Therefore, the slope of AB could be either +4/3 or -4/3. Two answers are possible here.

I suspect either something was not copied correctly from the source, or that the source is faulty.

Let me know if you have any questions.

Mike

It is 100% choice D because it is inferable that with the coordinate description (X,Z), (X,Y), (X+3,Y) that \(X=X\) and for Y to be parallel, the (X,Z) and (x+3,Y) relationship must be positive

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

19 Jan 2014, 15:18

1

This post received KUDOS

Expert's post

Archit143 wrote:

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

A. -4/3 B. 2/3 C. 1 D. 4/3 E. 2

Apparently Archit added this very important note after I wrote my initial response to the problem. As they say, a picture is worth a thousand words, and a GMAT math problem that includes a diagram often will make little or no sense without the diagram. The GMAT never gives you a diagram unless there's some crucial piece of information you need from the diagram: this is a very important point to appreciate.

With this added piece of information, it's perfectly clear that the answer is (A). If Z > Y, then the line must move DOWN from (X,Z) to (X+3, Y). That's the definition of a negative slope. With the analysis above, we saw that the slope would have to be either -4/3 or +4/3. With the information from the diagram it's clear that the slope is -4/3, answer = (A).

Please let me know if anyone has any further questions. Mike _________________

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

17 Jan 2015, 08:40

Archit143 wrote:

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

A. -4/3 B. 2/3 C. 1 D. 4/3 E. 2

In triangle ABC line AB is parallel to Y-axis and line BC is parallel to X axis . Z>Y so line AC will be in 1 st quadrant AC=5, BC= 3 and AB=\sqrt{(5^2-3^2)}=4 angle ACB, Tan(ACB)=4/3,NOTE : Slope of any line is always taken from positive x-axis in anticlockwise direction. Slope=tan(180-ACB)=-tan (ACB)=-4/3

_________________

"Arise, Awake and Stop not till the goal is reached"

Re: ABC is a right angle triangle, right angled at B Co ordinate [#permalink]

Show Tags

20 Feb 2015, 07:36

mikemcgarry wrote:

Archit143 wrote:

ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?

Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A.

A. -4/3 B. 2/3 C. 1 D. 4/3 E. 2

Apparently Archit added this very important note after I wrote my initial response to the problem. As they say, a picture is worth a thousand words, and a GMAT math problem that includes a diagram often will make little or no sense without the diagram. The GMAT never gives you a diagram unless there's some crucial piece of information you need from the diagram: this is a very important point to appreciate.

With this added piece of information, it's perfectly clear that the answer is (A). If Z > Y, then the line must move DOWN from (X,Z) to (X+3, Y). That's the definition of a negative slope. With the analysis above, we saw that the slope would have to be either -4/3 or +4/3. With the information from the diagram it's clear that the slope is -4/3, answer = (A).

Please let me know if anyone has any further questions. Mike

Sorry i did not understand quite well . Pls note fig is drawn in 1st quadrant with Z > Y i.e point B is above A. how can point B lie above A if Z>Y ? A, B are (X,Z), (X,Y) _________________

Thanks, Lucky

_______________________________________________________ Kindly press the to appreciate my post !!

MBA Admission Calculator Officially Launched After 2 years of effort and over 1,000 hours of work, I have finally launched my MBA Admission Calculator . The calculator uses the...

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

The London Business School Admits Weekend officially kicked off on Saturday morning with registrations and breakfast. We received a carry bag, name tags, schedules and an MBA2018 tee at...