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) & stem:[(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

Plug 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

9

Choice-A

This is the correct answer, as it exactly matches the computed distance

Correct \$\sqrt(20)\$

10

Choice-B

This is too small and does not account for the actual distance between the points

Wrong \$\sqrt(2)\$

11

Choice-C

This value does not correspond to the sum of the squares of the differences in coordinates

Wrong \$\sqrt(11)\$

12

Choice-D

This option is incorrect, as it underestimates the distance calculated

Wrong \$\sqrt(12)\$

13

Answer

Option

A

14

Sumup

Please summarize choices