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What is the area of a triangle created by the intersections

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What is the area of a triangle created by the intersections [#permalink] New post 08 Jan 2019, 08:53
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Question Stats:

37% (00:59) correct 62% (00:15) wrong based on 8 sessions
What is the area of a triangle created by the intersections of the lines \(x=4\), \(y=5\) and \(y = -\frac{3}{4}x + 20\)?

A. 42
B. 54
C. 66
D. 72
E. 96
[Reveal] Spoiler: OA

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Re: What is the area of a triangle created by the intersections [#permalink] New post 08 Jan 2019, 18:46
Expert's post
GreenlightTestPrep wrote:
What is the area of a triangle created by the intersections of the lines \(x=4\), \(y=5\) and \(y = -\frac{3}{4}x + 20\)?

A. 42
B. 54
C. 66
D. 72
E. 96



x=4 and y=5 are perpendicular lines so we have a right angled triangle at their intersection.

Now the height will be on x=4 and will be till \(y = -\frac{3}{4}x + 20\) intersects it. So, when x=4, \(y = -\frac{3}{4}*4 + 20=17\)..
Height is Displacement in y coordinates = 17-5=12


Now the base will be on y=5 and will be till \(y = -\frac{3}{4}x + 20\) intersects it. So, when y=5, \(5= -\frac{3}{4}*x + 20=17....5-20=\frac{-3}{4}x.....x=\frac{15*4}{3}=20\)..
Base is Displacement in x coordinates = 20-4=16..

Area = \(\frac{1}{2}*16*12=96\)

E
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GRE Instructor
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Re: What is the area of a triangle created by the intersections [#permalink] New post 09 Jan 2019, 06:37
Expert's post
GreenlightTestPrep wrote:
What is the area of a triangle created by the intersections of the lines \(x=4\), \(y=5\) and \(y = -\frac{3}{4}x + 20\)?

A. 42
B. 54
C. 66
D. 72
E. 96


Let's first sketch the lines x = 4 and y = 5
Image

To find the point where y = (-3/4)x + 20 intersects the line x = 4, replace x with 4 to get: y = (-3/4)4 + 20 = 17
So the point of intersection is (4, 17)

To find the point where y = (-3/4)x + 20 intersects the line y = 5, replace y with 5 to get: 5 = (-3/4)x + 20
When we solve for x, we get x = 20
So the point of intersection is (20, 5)

Add this information to our sketch:
Image

From here, we can determine the length of the right triangle's base and height:
Image

Area = (1/2)(base)(height)
= (1/2)(16)(12)
= 96

Answer: E


Cheers,
Brent
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Re: What is the area of a triangle created by the intersections   [#permalink] 09 Jan 2019, 06:37
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