Chapter 12.8, Problem 25E

To determine

To find: The coordinates to make a coordinate proof to complete.

Answer to Problem 25E

The coordinate $\left(5d,-5d\right)$ makes the proof easier.

Explanation of Solution

Given information:

The coordinates of a triangle $\left(5d-5d\right),\left(0,-5d\right),\left(5d,0\right)$ .

  

To make a coordinate proof easier the vertex $\left(5d,-5d\right)$ of a triangle shifted to the origin $\left(0,0\right)$ . This will not change the shape of the triangle. The legs of the triangle is $5d\text{}\text{units}$ . The hypotenuse is given by sing the Pythagoras theorem.

  $H^2=B^2+P^2$

Here,

The value of $B$ and $P$ is $5d\text{units}$ . Substitute the value in the given formula,

   $\begin{array}{c}{H}^2=B^2+P^2\end{array}$

    $\begin{array}{c}={\left(5d\right)}^2+{\left(5d\right)}^2\end{array}$

    $\begin{array}{c}=50d^2\end{array}$

    $\begin{array}{c}=5d\sqrt{2}\end{array}$

Therefore, the coordinate $\left(5d,-5d\right)$ shifted to the origin makes the proof easier.