Tricky coordinate geometry problem

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Tricky coordinate geometry problem

by Nijo » Fri Jun 27, 2014 3:50 am
Hi
I am unable to solve the below problem, the OA is 96 but I cant get the figure right I think:

What is the area of a triangle created by the intersections of the lines x=4, y=5, and y=−34x+20?

Could anyone pl help? Thanks
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by GMATGuruNY » Fri Jun 27, 2014 4:21 am
Note the correction in red:
What is the area of a triangle created by the intersections of the lines x=4, y=5 and y=−3/4x+20?

A)42

B)54

C)66

D)72

E)96

OA to follow
DRAW the figure:
Image

Vertex A is the intersection of x=4 and y=5:
(4.5).

Vertex B is the intersection of x=4 and y=(-3/4)x + 20.
Plugging x=4 into y=(-3/4)x + 20, we get:
y = (-3/4)4 + 20
y = 17.
Thus, the coordinates of vertex B are (4,17).

Vertex C is the intersection of y=5 and y=(-3/4)x + 20.
Plugging y=5 into y=(-3/4)x + 20, we get:
5 = (-3/4)x + 20
-15 = (-3/4)x
-60 = -3x
x = 20.
Thus, the coordinates of vertex C are (20,5).

In triangle ABC, AC=16 and AB=12.
Thus, the area of triangle ABC = (1/2)(16)(12) = 96.

The correct answer is E.
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by Nijo » Fri Jun 27, 2014 7:32 am
Got it, thanks very much