Chapter 9.1, Problem 24PPS

To determine

To find: The distance from the toe board to the center of the circle.

Answer to Problem 24PPS

The distance from the toe board to the center of the circle is $4.528\text{ units}$

Explanation of Solution

Given:

The coordinates is given as,

  $\left(-4,1\right)\left(5,2\right)$

Calculation:

The coordinates of the mid-point is calculated as,

  $\begin{array}{c}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{-4+5}{2},\frac{1+2}{2}\right)\\ =\left(\frac{1}{2},\frac{3}{2}\right)\\ =\left(0.5,1.5\right)\end{array}$

Calculate the distance using the distance formula.

  $\begin{array}{c}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(0.5-\left(-4\right)\right)}^2+{\left(1.5-1\right)}^2}\\ =\sqrt{{\left(4.5\right)}^2+{\left(0.5\right)}^2}\\ =\sqrt{20.50}\end{array}$

Solve further as,

  $\begin{array}{c}d=\mathrm{4.5276925...}\\ =4.528\text{ units}\end{array}$

Thus, the distance from the toe board to the center of the circle is $4.528\text{ units}$