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If a triangle in the xy-coordinate system has vertices at (-2 , -3), (4, -3) and (28, 7), what is the area of the triangle?
A. 30
B. 36
C. 48
D. 60
E. 65
Kudos for a correct solution.
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A. 30
B. 36
C. 48
D. 60
E. 65
Kudos for a correct solution.
_________________
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Bunuel
MAGOOSH OFFICIAL SOLUTION:
Attachment:
areaoftriangle_text.PNG [ 16.56 KiB | Viewed 13483 times ]
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General Discussion
Let's say A is (-2,-3), B is (4,-3) and C is (28,7).
If we quickly plot A, B and C on co-ordinate system, it's obvious that A and B are parallel to x-axis. So, length of AB is 6.
Let AB be the base, then height of triangle will be length of perpendicular from C on AB. But since AB is parallel to x-axis, it'll be just (7-(-3)) = 10.
So area = (1/2)*6*10.
If we quickly plot A, B and C on co-ordinate system, it's obvious that A and B are parallel to x-axis. So, length of AB is 6.
Let AB be the base, then height of triangle will be length of perpendicular from C on AB. But since AB is parallel to x-axis, it'll be just (7-(-3)) = 10.
So area = (1/2)*6*10.
Bunuel
attached pic for solution
answer A
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Posts: 1,776
Bunuel
(-2,-3) is in 3rd quadrant, (4,-3) is in 4th quadrant while (28,7) is in 1st quadrant.
Also, y coordinate of (-2,-3) and (4,-3) is same so they lie on same horizontal line.
So base of triangle = sqrt[(-3+3)^2 + (4+2)^2] = 6
And height of triangle = 7 - (-3)
= 10
So area of triangle = 1/2*6*10
= 30
Hence option (A),
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Expert reply
Posts: 22,740
Bunuel
Solution:
We can let A = (-2 , -3), B = (4, -3), and C = (28, 7). Since A and B have the same y-coordinates, we should let AB be the base of the triangle and hence AB = |4 - (-2)| = 6. Now, no matter where C is, the height of the triangle is the absolute difference between the y-coordinates of A (or B) and C. That is, the height of the triangle is |7 - (-3)| = 10. Therefore, the area of the triangle is ½ x 6 x 10 = 30.
Answer: A
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