Question

use the right triangle abc to find the length of the line segment between point a and point b. you can think of the distance between point a and point b 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. b (-1,5) c (7,5) a (7,-3)

Explanation:

Step1: Find length of AC

Points A(7, -3) and C(7, 5) have same x - coordinate. The distance formula for vertical line is $|y_2 - y_1|$. So $AC=|5 - (-3)|=|8| = 8$.

Step2: Find length of BC

Points B(-1, 5) and C(7, 5) have same y - coordinate. The distance formula for horizontal line is $|x_2 - x_1|$. So $BC=|7-(-1)| = |8|=8$.

Step3: Find length of AB (hypotenuse)

Using Pythagorean theorem $AB=\sqrt{AC^{2}+BC^{2}}$. Substitute $AC = 8$ and $BC = 8$. So $AB=\sqrt{8^{2}+8^{2}}=\sqrt{64 + 64}=\sqrt{128}=8\sqrt{2}\approx11.31$ (or if we consider the first part about AC length, for AC length the answer is 8).

Answer:

For length of AC: 8; For length of AB: $8\sqrt{2}$ (or approximately 11.31). (Since the question first asks about AC length and then AB, if we take AC length as the answer for the sub - question "What is the length of the line segment between point A and point C?": 8)