Question

use the right triangle abc to find the length of the line segment between point b and point c
now that youve 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. what is the length of the line segment between point b and point c? use square root notation to write the exact value. label that on the coordinate plane. you can solve on paper and then enter your answer on zearn.
image of coordinate plane with points a(4, -3), b(8, -3), c(4, 6) forming a right triangle, leg lengths 4 and 9 marked

Explanation:

Step1: Identify the legs' lengths

From the graph, leg \( AB \) has length \( 4 \) (horizontal distance: \( 8 - 4 = 4 \)) and leg \( AC \) has length \( 9 \) (vertical distance: \( 6 - (-3) = 9 \)).

Step2: Apply Pythagorean Theorem

The Pythagorean Theorem states \( c^2 = a^2 + b^2 \), where \( a = 4 \), \( b = 9 \), and \( c \) is the hypotenuse \( BC \). So \( c^2 = 4^2 + 9^2 = 16 + 81 = 97 \). Then \( c = \sqrt{97} \).

Answer:

\(\sqrt{97}\)