Question

determine the distance between the points (-2, 3) and (5, - 3).

9

√15

80

49

√85

Explanation:

Step1: Recall Distance Formula

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

Step2: Identify Coordinates

Let \((x_1, y_1) = (-2, 3)\) and \((x_2, y_2) = (5, -3)\).

Step3: Substitute into Formula

Calculate \( x_2 - x_1 = 5 - (-2) = 7 \) and \( y_2 - y_1 = -3 - 3 = -6 \).
Then, \( d = \sqrt{(7)^2 + (-6)^2} = \sqrt{49 + 36} = \sqrt{85} \).

Answer:

\(\sqrt{85}\) (corresponding to the option with \(\sqrt{85}\))