Q168 / 270 · NDA 2012 (Phase 1) · Mathematics

If the mid point between the points $(a+b, a-b)$ and $(-a, b)$ lies on the line $a x+b y=k$, what is $k$ equal to?

  • A
    $a / b$
  • B
    $a+b$
  • Correct answer
    C
    $a b$
  • D
    $a-b$

Solution

Mid point is $\left(\frac{a+b-a}{2}, \frac{a-b+b}{2}\right)$ $=\left(\frac{b}{2}, \frac{a}{2}\right)$ it lies on $a x+b y=k$ $\begin{aligned} a\left(\frac{b}{2}\right)+b\left(\frac{a}{2}\right) & =k \\ k & =a b \end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions