Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points in simplest radical form. (-5,5) and (4,-7) click twice to draw a line. click a segment to erase it. answer attempt 1 out of 2 leg 1: leg 2: hypotenuse: submit answer

Explanation:

Step1: Find the difference in x - coordinates

Let $(x_1,y_1)=(-5,5)$ and $(x_2,y_2)=(4, - 7)$. The difference in x - coordinates $\Delta x=x_2 - x_1=4-(-5)=9$.

Step2: Find the difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=-7 - 5=-12$.

Step3: Calculate the lengths of the legs

The lengths of the legs of the right - triangle are the absolute values of $\Delta x$ and $\Delta y$. Leg 1: $| \Delta x| = 9$, Leg 2: $|\Delta y| = 12$.

Step4: Use the Pythagorean theorem to find the hypotenuse

By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 9$ and $b = 12$. So $c=\sqrt{9^{2}+12^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$.

Answer:

Leg 1: 9
Leg 2: 12
Hypotenuse: 15