Co-ordinate geometry -2

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guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Mon Apr 22, 2013 7:05 am

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?

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

OA A

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Source: Beat The GMAT — Problem Solving | Mon Apr 22, 2013 7:05 am

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 22, 2013 7:43 am

guerrero 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?

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

Are you sure?
If Z > Y, then as per the problem statement, point A will be above point B because coordinates of A and B are (X, z) and (X, Y).

If that is the case, then refer to the following diagram,

So, AC will have a negative slope.

Only option A works.
[spoiler]
The correct answer is A.[/spoiler]

Anju Agarwal
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guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Mon Apr 22, 2013 8:06 am

Anju@Gurome wrote:
guerrero wrote:
Are you sure?
If Z > Y, then as per the problem statement, point A will be above point B because coordinates of A and B are (X, z) and (X, Y).

If that is the case, then refer to the following diagram,

So, AC will have a negative slope.

Only option A works.
[spoiler]
The correct answer is A.[/spoiler]
Thanks Anju , this was really simple . The statement kind of confused me .Source is Grockit . I will review it .

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coolanujdel: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Thu Aug 26, 2010 11:58 pm

by coolanujdel » Tue Oct 29, 2013 2:32 am

guerrero wrote:
Anju@Gurome wrote:
guerrero wrote:
Are you sure?
If Z > Y, then as per the problem statement, point A will be above point B because coordinates of A and B are (X, z) and (X, Y).

If that is the case, then refer to the following diagram,

So, AC will have a negative slope.

Only option A works.
[spoiler]
The correct answer is A.[/spoiler]
Thanks Anju , this was really simple . The statement kind of confused me .Source is Grockit . I will review it .
How did you know that slope is negative, means how did you get the direction that for Y it will go down?

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mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Tue Oct 29, 2013 3:38 am

coolanujdel wrote: How did you know that slope is negative, means how did you get the direction that for Y it will go down?

For the GMAT it is very useful to know how a line with a particular slope (positive, negative, zero) actually looks like:

Thus it was easier to select a negative value as the answer.

For more details on this you can read this article : https://www.cliffsnotes.com/math/geometr ... -of-a-line

To calculate the value of the slope:
Referring to the image provided by Anju in the above posts:

We know that X = 3, AC = 5
Thus,
co-ordinate of B = (3, Y)
co-ordinate of C = (6, Y)

The distance BC can be found out from above : BC = 3
Also AB = 4 (Using the property of 3-4-5 right angled triangle)

The new diagram with the co-ordinates updated:

Now, Slope of a line = Rise/Run

Slope of AC = [ y - (y + 4) ] / [ 6 - 3 ] = [spoiler]-4/3 is the slope[/spoiler]

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