megafan wrote:
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)
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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