Question

PQ has endpoints P(-4, -2) and Q(-6, 8). What is the length of segment PQ in simplest radical form?

Answer 1

Answer:

The answer is

$2 \sqrt{26} \: \: \: \: units$

Step-by-step explanation:

The distance between two points of a line segment can be found by using the formula

$d = \sqrt{ ({x_1 - x_2})^{2} + ({y_1 - y_2})^{2} }$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

P(-4, -2) and Q(-6, 8)

The length of the line segment is

$|PQ| = \sqrt{ ({ - 4 + 6})^{2} + ({ - 2 - 8})^{2} } \\ = \sqrt{ {2}^{2} + ({ - 10})^{2} } \\ = \sqrt{4 + 100} \\ = \sqrt{104} \: \: \: \: \: \: \: \\ = 2 \sqrt{26} \: \: \: \: \: \: \:$

We have the final answer as

$2 \sqrt{26} \: \: \: \: units$

Hope this helps you