Question

1. graph a right triangle with the points (3,3) and (8, - 9) forming the hypotenuse. using the sides, find the distance between the two points in simplest radical form.

leg 1: __ leg 2: hypotenuse: __

Explanation:

Step1: Find the length of horizontal leg

The difference in x - coordinates gives the length of the horizontal leg. Let $(x_1,y_1)=(3,3)$ and $(x_2,y_2)=(8, - 9)$. The length of the horizontal leg (Leg 1) is $|x_2 - x_1|=|8 - 3| = 5$.

Step2: Find the length of vertical leg

The difference in y - coordinates gives the length of the vertical leg. The length of the vertical leg (Leg 2) is $|y_2 - y_1|=|-9 - 3|=12$.

Step3: Use the Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. Here $a = 5$ and $b = 12$. So $c=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13$.

Answer:

Leg 1: 5
Leg 2: 12
Hypotenuse: 13