Chapter E, Problem 10.1EX

To determine

To find the locus of points equidistant from two given points.

Answer to Problem 10.1EX

Option (c)

Explanation of Solution

Given information: Two points $a$ and $b$ in a plane.

Let $x$ be any point in plane, then

  $\begin{array}{l}$ {(x-a)}^2={(x-b)}^2$x^2+a^2-2ax=x^2+b^2-2bx\\ 2bx-2ax=b^2-a^2\\ 2(b-a)x=(b+a)(b-a)\\ x=\frac{(b+a)}{2}\end{array}$

Hence, $x$ is the point which bisecting the line.