Question

calculate the distance between the points m=(-5, -6) and p=(2, 2) 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 \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( x_1 = -5, y_1 = -6, x_2 = 2, y_2 = 2 \).

Step2: Substitute values into formula

Substitute into the formula: \( d = \sqrt{(2 - (-5))^2 + (2 - (-6))^2} \).
Simplify inside the square root: \( 2 - (-5) = 7 \), \( 2 - (-6) = 8 \).
So, \( d = \sqrt{7^2 + 8^2} \).

Step3: Calculate squares and sum

Calculate \( 7^2 = 49 \), \( 8^2 = 64 \).
Sum: \( 49 + 64 = 113 \).
Thus, \( d = \sqrt{113} \).

Answer:

\(\sqrt{113}\)