Question
Quantitative Aptitude Question on Geometry
The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
A
-5
B
-6
C
-7
D
-8
Answer
-8
Explanation
Solution
The correct answer is (D):
In a rectangle, diagonals bisect each other, so one diagonal should pass through the midpoint of the other. Midpoint of the diagonal connecting (2, 5) and (6, 3)
= (2+6/2, 5+3/2) = (4,4)
The other diagonal, y = 3x + c should also pass through (4, 4).
On substitution, 4 = 3 (4) + c ⇒ -8.