Question

use the right triangle abc to find the length of the line segment between point a and point b, between point a and point b. start by substituting the values you know and the value you dont know into the equation. the hypotenuse is unknown, so you can use the variable c to represent the hypotenuse. the pythagorean theorem says that if a, b, and c are the sides of the right triangle, where c is the hypotenuse, then: $a^2 + b^2 = c^2$. point a (8, 3), point b (-2, -5), point c (8, -5). $a^2 + b^2 = c^2$ with boxes to fill in: $square^2 + square^2 = square^2$

Explanation:

Step1: Find the length of AC

Point A is (8, 3) and point C is (8, -5). The distance between them (length of AC) is the difference in y - coordinates: $|3 - (-5)| = 8$. So one leg (a or b) is 8.

Step2: Find the length of BC

Point B is (-2, -5) and point C is (8, -5). The distance between them (length of BC) is the difference in x - coordinates: $|8 - (-2)| = 10$. So the other leg (a or b) is 10.

Step3: Substitute into Pythagorean theorem

The hypotenuse c is the distance between A and B. Substitute a = 10, b = 8 (or vice - versa) into $a^{2}+b^{2}=c^{2}$. So we get $10^{2}+8^{2}=c^{2}$ (or $8^{2}+10^{2}=c^{2}$).

Answer:

$10^{2}+8^{2}=c^{2}$ (or $8^{2}+10^{2}=c^{2}$, where the first two boxes can be 10 and 8 (in any order) and the third box is c)