Chapter 1.3, Problem 62PPS

To determine

To Find: The name for the point that satisfies the given condition.

Answer to Problem 62PPS

The required point are $\left(0,-4\right),\left(0,10\right)$ .

Explanation of Solution

Given:

The two points on the y axis that are 25 unitsfrom $\left(-24,3\right)$ .

Calculation:

Consider $\left(0,y\right)$ is the point on the y axis.

Then, the distance between the two points is,

  $\begin{array}{l}d=\sqrt{{\left(0-\left(-24\right)\right)}^2+\left(y-3\right)}\\ 25=\sqrt{576{\left(y-3\right)}^2}\\ 625-576={\left(y-3\right)}^2\\ y+3=\pm 7\end{array}$

Solve further as,

  $y=-4,10$

Thus, the required point are $\left(0,-4\right),\left(0,10\right)$ .