Question

The point Q$\left(x,y\right)$ is equidistant from two points P $\left(a+b,b-a\right)$and R $\left(a-b,a+b\right)$ such that P,Q,R lies on same straight line drawn on cartesian plane, then value of $\left(x,y\right)$ will be

• A. $\left(\frac{a}{2},\frac{b}{2}\right)$
• B. $\left(a,b\right)$
• C. $\left(\frac{a+b}{2},\frac{a-b}{2}\right)$
• D. $\left(\frac{b}{2},\frac{a}{2}\right)$

Answer 1

The correct option is B $\left(a,b\right)$

Since points P,Q,R lie on same straight line and Q is at equal distance from both P and R , which means Q is mid point of P and R.

So, mid point of any two points is average of both the points P and R respectively.

Value of Q $\left(x,y\right)$ will be $\left(\frac{\left(a-b\right)+\left(a+b\right)}{2},\frac{\left(b-a\right)+\left(a+b\right)}{2}\right)=\left(\frac{a+a+b-b}{2},\frac{b+b+a-a}{2}\right)=\left(a,b\right)$