Chapter 6.5, Problem 49HP

To determine

To calculate:

The vertices of a square with diagonals

Answer to Problem 49HP

The vertices of a square are $\left(0,0\right),\left(0,6\right),\left(6,0\right),\left(6,6\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}\mathrm{y}=\mathrm{x}\\ \mathrm{y}=-\mathrm{x}+6\end{array}$

Calculation:

Here, need to graph the lines $\mathrm{y}=\mathrm{x}$ and $\mathrm{y}=-\mathrm{x}+6$ . There are six units from the origin to $\mathrm{y}$ and $\mathrm{x}$ -intercept of $\mathrm{y}=-\mathrm{x}+6$ .

Thus, three vertices of the square are defined as $\left(0,0\right),\left(0,6\right),\left(6,0\right)$ . $\left(6,6\right)$ is above the point $\left(6,0\right)$ by $6$ units.

Therefore, the four vertices of square are $\left(0,0\right),\left(0,6\right),\left(6,0\right),\left(6,6\right)$ which has perpendicular diagonals. These are the points which are located at the equidistant from the intersection of lines.