Question

find the distance between the points (-10, 6) and (-4, -5). write your answer as a whole number or a fully simplified radical expression. do not round.

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

Here, \( x_1 = -10 \), \( y_1 = 6 \), \( x_2 = -4 \), \( y_2 = -5 \).

Step3: Substitute into formula

\( d = \sqrt{(-4 - (-10))^2 + (-5 - 6)^2} \)
\( = \sqrt{(6)^2 + (-11)^2} \)

Step4: Simplify squares

\( = \sqrt{36 + 121} \)

Step5: Add inside radical

\( = \sqrt{157} \)

Answer:

\(\sqrt{157}\)