Question

what is the distance between points p and r? 5√13 units, √14 units, 10√13 units, √130 units

Explanation:

Step1: Identify coordinates of P and R

From the grid, assume point \( P \) has coordinates \((-9, 3)\) and point \( R \) has coordinates \((1, -2)\) (or use the right triangle legs: horizontal change \( \Delta x = 10 \), vertical change \( \Delta y = 5 \)).

Step2: Apply distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Substituting \( \Delta x = 10 \), \( \Delta y = 5 \), we get \( d = \sqrt{10^2 + 5^2} = \sqrt{100 + 25} = \sqrt{125} = 5\sqrt{13} \).

Answer:

$5\sqrt{13}$ units