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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
What is the area of a triangle created by the intersections
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08 Jan 2019, 08:53
08 Jan 2019, 08:53
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Question Stats:
79% (02:41) correct
20% (02:28) wrong based on 73 sessions
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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
A. 42
B. 54
C. 66
D. 72
E. 96
Re: What is the area of a triangle created by the intersections
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08 Jan 2019, 18:46
08 Jan 2019, 18:46
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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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
What is the area of a triangle created by the intersections
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09 Jan 2019, 06:37
09 Jan 2019, 06:37
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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
A. 42
B. 54
C. 66
D. 72
E. 96
Let's first sketch the lines x = 4 and y = 5
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:
From here, we can determine the length of the right triangle's base and height:
Area = (1/2)(base)(height)
= (1/2)(16)(12)
= 96
Answer: E
Cheers,
Brent
