Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points in sim
$(-4,7)$ and $(2,9)$
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 horizontal and vertical distances (legs)

The horizontal distance (leg 1) is calculated by \(|x_2 - x_1|\). Here, \(x_1=-4\) and \(x_2 = 2\), so \(|2-(-4)|=|2 + 4|=6\).
The vertical distance (leg 2) is calculated by \(|y_2 - y_1|\). Here, \(y_1 = 7\) and \(y_2=9\), so \(|9 - 7|=2\).

Step2: Use the Pythagorean theorem to find the hypotenuse (distance between the two points)

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 6\) (leg 1) and \(b = 2\) (leg 2).

$$c=\sqrt{6^{2}+2^{2}}=\sqrt{36 + 4}=\sqrt{40}=2\sqrt{10}$$

Answer:

Leg 1: \(6\), Leg 2: \(2\), Hypotenuse: \(2\sqrt{10}\)