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If the area of right triangle ABC is 30, what are the coordi

by GMATinsight » Mon Oct 12, 2015 10:52 pm
If the area of right triangle ABC is 30, what are the coordinates of point B ?

A. (9, 4)
B. (4, 9)
C. (3, 4)
D. (-3, 9)
E. (12, 4)

Answer: Option A
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by GMATinsight » Mon Oct 12, 2015 10:53 pm
GMATinsight wrote:If the area of right triangle ABC is 30, what are the coordinates of point B ?

A. (9, 4)
B. (4, 9)
C. (3, 4)
D. (-3, 9)
E. (12, 4)

Answer: Option A
Point B will have same Y co-ordinate as Point A has i.e. 4. Hence, Option A, C and E remaining and other two options B and D are ruled out

Area of Triangle ABC = (1/2)*AB*AC = 30 (Given)

But AC = 5 (Distance of Y co-ordinate from -1 to 4 as X co-ordinates of A and C are same)

i.e. Area of Triangle ABC = (1/2)*AB*5 = 30 i.e. AB = 12

Horizontal Distance of 12 from X co-ordinate of point A (-3) = -3+12 = +9

i.e. Co-ordinate of point B = (9, 4)

Answer: Option A
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