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

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

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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Source: Beat The GMAT — Problem Solving | Mon Oct 12, 2015 10:52 pm

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

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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