Question

example 3: what are the lengths of the hypotenuse of triangle abc? data points: a(-4, 4), b(-4, -2), c(4, -2) use the distance formula to calculate the length of ac. $d = \sqrt{(-2 - 4)^2 + (4 - (-4))^2}$ $d = \sqrt{36 + 64}$ $d = \sqrt{100}$ $d = 10$ therefore, the length of the hypotenuse, side $\overline{ac}$, is 10.

Explanation:

Step1: Recall distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute $A(-4,4), C(4,-2)$

$d=\sqrt{(4-(-4))^2+(-2-4)^2}$

Step3: Simplify inside the root

$d=\sqrt{(8)^2+(-6)^2}=\sqrt{64+36}$

Step4: Calculate final value

$d=\sqrt{100}=10$

Answer:

10