Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance in radical form. (-9,6) and (-5,4) 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 length of leg 1 (horizontal side)

Find the difference in x - coordinates. Let \((x_1,y_1)=(-9,6)\) and \((x_2,y_2)=(-5,4)\). The length of leg 1 \(d_x=\vert x_2 - x_1\vert=\vert-5-(-9)\vert=\vert-5 + 9\vert = 4\).

Step2: Find the length of leg 2 (vertical side)

Find the difference in y - coordinates. The length of leg 2 \(d_y=\vert y_2 - y_1\vert=\vert4 - 6\vert=2\).

Step3: Find the length of the hypotenuse

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 4\) and \(b = 2\). So \(c=\sqrt{4^{2}+2^{2}}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}\).

Answer:

Leg 1: 4
Leg 2: 2
Hypotenuse: \(2\sqrt{5}\)