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. (-9, 6) and (-5, 4) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find the length of Leg 1 (horizontal distance)

The horizontal distance between the points \((-9,6)\) and \((-5,4)\) is the absolute difference of the \(x\)-coordinates. So, \(|-5 - (-9)| = |4| = 4\).

Step2: Find the length of Leg 2 (vertical distance)

The vertical distance between the points is the absolute difference of the \(y\)-coordinates. So, \(|4 - 6| = |-2| = 2\).

Step3: Find the length of the Hypotenuse (distance between the points)

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), substitute \(x_1 = -9\), \(y_1 = 6\), \(x_2 = -5\), \(y_2 = 4\).
\[

$$\begin{align*} d&=\sqrt{(-5 - (-9))^2 + (4 - 6)^2}\\ &=\sqrt{(4)^2 + (-2)^2}\\ &=\sqrt{16 + 4}\\ &=\sqrt{20}\\ &= 2\sqrt{5} \end{align*}$$

\]

Answer:

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