Question

find the distance between the points c(-6, 5) and d(-3, 1). the distance between the two points is \boxed{}.

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For points \( C(-6, 5) \) and \( D(-3, 1) \), let \( x_1 = -6 \), \( y_1 = 5 \), \( x_2 = -3 \), \( y_2 = 1 \).

Step2: Substitute values into formula

Calculate \( x_2 - x_1 = -3 - (-6) = -3 + 6 = 3 \) and \( y_2 - y_1 = 1 - 5 = -4 \). Then, \( d = \sqrt{(3)^2 + (-4)^2} \).

Step3: Simplify the expression

Compute \( 3^2 = 9 \) and \( (-4)^2 = 16 \). So, \( d = \sqrt{9 + 16} = \sqrt{25} = 5 \).

Answer:

5