Question

use the right triangle abc to find the length of the line segment between point b and point c.
you can think of the distance between point b and point c as the length of a hypotenuse of a right triangle. start by finding the length of the legs of this right triangle. what is the length of the line segment between point a and point c? label the length on the coordinate plane.
c (4,6)
a (4, -3)
b (8, -3)

Explanation:

Step1: Find length of AC

Points A(4, -3) and C(4, 6) have same x - coordinate. So length of AC is difference in y - coordinates.
Length of AC = \(|6 - (-3)| = |6 + 3| = 9\)

Step2: Find length of AB

Points A(4, -3) and B(8, -3) have same y - coordinate. So length of AB is difference in x - coordinates.
Length of AB = \(|8 - 4| = 4\)

Step3: Find length of BC (using Pythagorean theorem)

In right triangle ABC, \(BC^{2}=AB^{2}+AC^{2}\)
We know AB = 4 and AC = 9. So \(BC^{2}=4^{2}+9^{2}=16 + 81 = 97\)
Then \(BC=\sqrt{97}\approx9.85\) (But first, for the length of AC, the answer is 9)

Answer:

The length of the line segment between point A and point C is 9.