Question

1. describe the process used to find the distance between two points, then find the distance.

Explanation:

Step1: Recall Distance Formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify Coordinates

For point \( P(-2, 2) \), \( x_1 = -2 \), \( y_1 = 2 \). For point \( Q(5, 8) \), \( x_2 = 5 \), \( y_2 = 8 \).

Step3: Substitute into Formula

Calculate \( x_2 - x_1 = 5 - (-2) = 7 \) and \( y_2 - y_1 = 8 - 2 = 6 \). Then, \( d = \sqrt{7^2 + 6^2} \).

Step4: Simplify

\( 7^2 = 49 \), \( 6^2 = 36 \), so \( 49 + 36 = 85 \). Thus, \( d = \sqrt{85} \approx 9.22 \).

Answer:

The distance between \( P(-2, 2) \) and \( Q(5, 8) \) is \( \sqrt{85} \) (or approximately \( 9.22 \)). The process involves using the distance formula, identifying the coordinates of the two points, substituting them into the formula, and simplifying.