Question

calculate the distance between the points g = (-2, -2) and n = (1, -6) in the coordinate plane. give an exact answer (not a decimal approximation).

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

For \( G = (-2, -2) \), \( x_1 = -2 \), \( y_1 = -2 \); for \( N = (1, -6) \), \( x_2 = 1 \), \( y_2 = -6 \).

Step3: Substitute into formula

\( d = \sqrt{(1 - (-2))^2 + (-6 - (-2))^2} = \sqrt{(3)^2 + (-4)^2} \)

Step4: Simplify

\( \sqrt{9 + 16} = \sqrt{25} = 5 \)

Answer:

5