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megafan
Joined: 28 May 2009
Last visit: 15 Oct 2017
Posts: 137
Given Kudos: 91
Location: United States
Concentration: Strategy, General Management
Schools: Stern PT Fall'18 Booth PT '18
GMAT Date: 03-22-2013
GPA: 3.57
WE:Information Technology (Consulting)
06 Mar 2013, 11:13
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
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79% (02:15) correct
21%
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On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and an area of 30. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?
(A) (−6, −5)
(B) (−5, 12)
(C) (6, −9)
(D) (9, −8)
(E) (10, −3)
(A) (−6, −5)
(B) (−5, 12)
(C) (6, −9)
(D) (9, −8)
(E) (10, −3)
06 Mar 2013, 11:39
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The area of the triangle so formed will be = 1/2 x base x height = 1/2 x |(X-coordinate of point C)| x |(Y-coordinate of point C)| = 30
=> |product of coordinates of point C| = 60
Choice B is the only option that leads to this, and is the answer.
Please note here that we need to use the modulus signs because we do not know if point A lies on the positive Y axis and if B lies on the positive X axis.
=> |product of coordinates of point C| = 60
Choice B is the only option that leads to this, and is the answer.
Please note here that we need to use the modulus signs because we do not know if point A lies on the positive Y axis and if B lies on the positive X axis.
06 Mar 2013, 11:53
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megafan
You could have B and A on either the positive/negative x and y axis respectively. So a total of 4 triangles are possible, which have a right angle at C. Now, for the rectangle OACB, where O is the origin, the area of the other triangle OAB will also be 30. Now the co-ordinate of B and A will be the (x,y) co-ordinates of C respectively. Thus, for B = (-5,0) and A = (0,12), we have the area of the triangle OAB as 30.
B.
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