Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the dist
$(-9,-4)$ and $(-2,2)$
click twice to draw a line. click a segment to erase it.
answer attempt 1 out of 2
leg 1: leg 2: hypotenuse:

Explanation:

Step1: Calculate the length of leg 1 (horizontal side)

The formula for the horizontal distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(|x_2 - x_1|\).
For the points \((-9,-4)\) and \((-2,2)\), \(x_1=-9\), \(x_2 = - 2\).
\(|x_2 - x_1|=|-2-(-9)|=|-2 + 9|=7\)

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

The formula for the vertical distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(|y_2 - y_1|\).
For the points \((-9,-4)\) and \((-2,2)\), \(y_1=-4\), \(y_2 = 2\).
\(|y_2 - y_1|=|2-(-4)|=|2 + 4|=6\)

Step3: Calculate the length of the hypotenuse

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 7\) (leg1), \(b=6\) (leg2).
\(c=\sqrt{7^{2}+6^{2}}=\sqrt{49 + 36}=\sqrt{85}\)

Answer:

Leg 1: \(7\), Leg 2: \(6\), Hypotenuse: \(\sqrt{85}\)