Question

ph a right triangle with the two points forming the hypotenuse. using ical form. (-9,9) and (-2,4) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find horizontal side - length

The difference in x - coordinates gives the length of the horizontal side. Let $(x_1,y_1)=(-9,9)$ and $(x_2,y_2)=(-2,4)$. The length of the horizontal side $a=\vert x_2 - x_1\vert=\vert-2-(-9)\vert=\vert-2 + 9\vert = 7$.

Step2: Find vertical side - length

The difference in y - coordinates gives the length of the vertical side. The length of the vertical side $b=\vert y_2 - y_1\vert=\vert4 - 9\vert=5$.

Step3: Use Pythagorean theorem to find hypotenuse length

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$, where $a = 7$ and $b = 5$. So $c=\sqrt{7^{2}+5^{2}}=\sqrt{49 + 25}=\sqrt{74}$.

Answer:

The length of the hypotenuse is $\sqrt{74}$