in a right triangle, the hypotenuse has endpoints ( p(-3,2) ) and ( q(1,-3) ). if ( r ) represents the third vertex in the triangle and ( r ) is located in the third quadrant, what is the length of ( pr )?

Question

Accepted Answer

# Explanation:
## Step1: Determine the coordinates of point R
Since it's a right - triangle and R is in the third quadrant, and the hypotenuse is PQ. The right - angle is at R. The x - coordinate of R is the same as the x - coordinate of P ($x=-3$) and the y - coordinate of R is the same as the y - coordinate of Q ($y = - 3$). So, $R(-3,-3)$

## Step2: Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
For points $P(-3,2)$ and $R(-3,-3)$, $x_1=-3,y_1 = 2,x_2=-3,y_2=-3$
Substitute into the formula:
$$
\begin{align*}
d&=\sqrt{(-3+3)^2+(-3 - 2)^2}\
&=\sqrt{0+(-5)^2}\
&=\sqrt{25}\
& = 5
\end{align*}
$$

# Answer:
$5$

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QUESTION IMAGE

Question

Explanation:

Step1: Determine the coordinates of point R

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Answer: