Question

Find a point which is equidistant from the points $A\left(-5,4\right)$ and $B\left(-1,6\right)$? How many such points are there?

Answer 1

Find the point using midpoint formula.

Let point $Q$ be equidistant from $A\left(-5,4\right)$ and $B\left(-1,6\right)$

Then, point $Q$ is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

$$\begin{gathered} Q=\left(\frac{-5-1}{2},\frac{4+6}{2}\right) \\ =\left(-3,5\right) \end{gathered}$$

And points lie on perpendicular bisector to the line joining $AtoB$ are equidistance from $A\text{and}B$.

So, there are infinite points which are equidistant from $AandB$

Hence, the point which is equidistant from $\mathit{A}\left(-5,4\right)$and $\mathit{B}\left(-1,6\right)$ is $\left(-3,5\right)$. and there are infinite points.