The image presents three separate problems, each asking us to find something related to two points, $P_1$ and $P_2$. However, the problem statement is incomplete. I will assume the task is to calculate the distance between the two points in each problem. Problem 13: $P_1(2, -5)$ and $P_2(-4, 3)$ Problem 14: $P_1(3, 2)$ and $P_2(0, -1)$ Problem 15: $P_1(0, -3)$ and $P_2(-1, 1)$

1. Problem Description

The image presents three separate problems, each asking us to find something related to two points, $P_1$ and $P_2$. However, the problem statement is incomplete. I will assume the task is to calculate the distance between the two points in each problem.

Problem 13: $P_1(2, -5)$ and $P_2(-4, 3)$

Problem 14: $P_1(3, 2)$ and $P_2(0, -1)$

Problem 15: $P_1(0, -3)$ and $P_2(-1, 1)$

2. Solution Steps

The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula:

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

Problem 13: $P_1(2, -5)$ and $P_2(-4, 3)$

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

$d = \sqrt{(-6)^2 + (8)^2}$

$d = \sqrt{36 + 64}$

$d = \sqrt{100}$

$d = 10$

Problem 14: $P_1(3, 2)$ and $P_2(0, -1)$

$d = \sqrt{(0 - 3)^2 + (-1 - 2)^2}$

$d = \sqrt{(-3)^2 + (-3)^2}$

$d = \sqrt{9 + 9}$

$d = \sqrt{18}$

$d = 3\sqrt{2}$

Problem 15: $P_1(0, -3)$ and $P_2(-1, 1)$

$d = \sqrt{(-1 - 0)^2 + (1 - (-3))^2}$

$d = \sqrt{(-1)^2 + (4)^2}$

$d = \sqrt{1 + 16}$

$d = \sqrt{17}$

3. Final Answer

Problem 13: 10

Problem 14: $3\sqrt{2}$

Problem 15: $\sqrt{17}$