1

Problem

Find the length of the line segment between points P(8, 5) and Q(4, 3).

2

Step

Let us the given points \$(x_1,y_1)\$ & \$(x_2,y_2)\$

(8, 5) and (4, 3)

3

Formula

To find the length of the line segment between two points, you can use the distance formula: \$d = \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\$.

4

Step

Substitute the values into the distance formula:

d = \$\sqrt((4 - 8)^2 + (3 - 5)^2)\$

\$d = \sqrt((- 4)^2 + (-2)^2)\$

5

Step

Solve for d:

\$d = \sqrt (16+ 4)\$

\$d = \sqrt(20)\$

6

Solution

So, the length of the line segment between points (8, 5) and (4, 3) is \$\sqrt(20)\$ .

7

Sumup

Please summarize steps

Choices

8

Choice-A

It is correct because it accurately represents the length of the line segment between points P and Q

Correct \$\sqrt(20)\$

9

Choice-B

This is the incorrect answer. The distance we calculated is \$\sqrt(20)\$, \$\sqrt 2\$

Wrong \$\sqrt(2)\$

10

Choice-C

This is the incorrect answer. The distance we calculated is \$\sqrt(20)\$, \$\sqrt 11\$

Wrong \$\sqrt(11)\$

11

Choice-D

This is the incorrect answer. The distance we calculated is \$\sqrt(20)\$, \$\sqrt 12\$

Wrong \$\sqrt(12)\$

12

Answer

Option

A

13

Sumup

Please summarize choices