Question

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

• A. 4
• B. 3
• C. -4
• D. -3
• E. 1

Answer 1

Answer: (C)

-4

Points $(2,5)$ and $(5,1)$ form a diagonal of the rectangle.

Hence, the mid point of these points will lie on the other diagonal.

Mid Point $=(\frac{2+5}{2},\frac{5+1}{2})=(\frac{7}{2},3)$

Equation of the other diagonal is $y=2x+k$

Therefore, $3=2\times \frac{7}{2}+k\Rightarrow k=-4$