Question

finding distances in the coordinate pla
use the right triangle abc to find the length of the line segment between point a and po
now that you’ve found the lengths of the legs of this right triangle, you can use the pythagorean
theorem to help you find the length of the hypotenuse. that’s the length of the line segment
between point a and point b. start by substituting the values you know and the value you don’t
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).

(the coordinate plane shows points: b(-2,5), c(7,5), a(7,-3). there is an equation (a^2 + b^2 = c^2) with blanks: (square^2 + square^2 = square^2))

Explanation:

Step1: Find length of horizontal leg

Points B(-2,5) and C(7,5) have same y - coordinate. Horizontal distance \( a=|7 - (-2)| = 9\)

Step2: Find length of vertical leg

Points C(7,5) and A(7,-3) have same x - coordinate. Vertical distance \( b = |5-(-3)|=8\)

Step3: Substitute into Pythagorean theorem

Substitute \(a = 9\), \(b = 8\) into \(a^{2}+b^{2}=c^{2}\), we get \(9^{2}+8^{2}=c^{2}\)

Answer:

\(9^{2}+8^{2}=c^{2}\) (where the first box is 9, the second box is 8, and the third box is \(c\))