Question

on square PQRS below, if Q is located at (7, 0) and R is located at (5, -8), what is the length of SRleave it in radical form

Answer 1

In a square, all the sides are the same length.

$PQ=QR=SR=SP$

So, to find the length of the segment SR you can find the length of the segment QR using the formula of the distance between two points, that is:

$\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}} \\ \text{ Where d is the distance between two points } \\ A(x_1,y_1)\text{ and} \\ B(x_2,y_2) \end{gathered}$

So, in this case, you have

$\begin{gathered} Q(7,0) \\ R(5,-8) \\ d=\sqrt[]{(5_{}-7)^2+(-8-0)^2} \\ d=\sqrt[]{(-2)^2+(-8)^2} \\ d=\sqrt[]{4+64} \\ d=\sqrt[]{68} \end{gathered}$

Therefore, the length of the segment SR is

$\sqrt[]{68}$