The points (2,5) and (5,1) are two opposite vertices of a rectangle. If other two vertices are points on the straight line y =2x + k , then the value of k is

Options

A. 4
B. 3
C. `-4`
D. `-3`

Answer

C

Explanation

Now, mid-point of A (2,5) and B(5,1) is
` C((2+5)/2, (5+1)/2) or C(7/2 , 3)`

We know that the diagonals of a rectangle bisect each other .
The mid-point C( ` 7/2, 3`) lies on a given line.
` Rightarrow 3=2 xx7/2+c=0`
` Rightarrow 3 =7 + k Rightarrow k =-4`