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. (-7,8) and (2,1) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find horizontal distance

The horizontal distance between the points $(-7,8)$ and $(2,1)$ is the difference in x - coordinates. Let $(x_1,y_1)=(-7,8)$ and $(x_2,y_2)=(2,1)$. The horizontal distance $d_x=\vert x_2 - x_1\vert=\vert2-(-7)\vert=\vert2 + 7\vert = 9$.

Step2: Find vertical distance

The vertical distance between the points is the difference in y - coordinates. So, $d_y=\vert y_2 - y_1\vert=\vert1 - 8\vert=\vert-7\vert = 7$.

Step3: Use the Pythagorean theorem

The distance $d$ between two points is the length of the hypotenuse of a right - triangle with legs $d_x$ and $d_y$. By the Pythagorean theorem $d=\sqrt{d_x^{2}+d_y^{2}}$. Substitute $d_x = 9$ and $d_y = 7$ into the formula: $d=\sqrt{9^{2}+7^{2}}=\sqrt{81 + 49}=\sqrt{130}$.

Answer:

$\sqrt{130}$