Question

answer attempt 1 out of 2
leg 1: 　　 leg 2: 　　 distance: 　　 submit answer

Explanation:

Step1: Identify coordinates of points

First, find the coordinates of the two yellow points. From the graph, the first point is at \((-6, 3)\) and the second is at \((-2, -4)\).

Step2: Calculate Leg 1 (vertical distance)

The vertical distance (change in y - coordinates) is \(|3 - (-4)| = |3 + 4| = 7\).

Step3: Calculate Leg 2 (horizontal distance)

The horizontal distance (change in x - coordinates) is \(|-6 - (-2)| = |-6 + 2| = |-4| = 4\).

Step4: Calculate Distance (using Pythagorean theorem)

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Substituting \(x_1=-6,y_1 = 3,x_2=-2,y_2=-4\), we get \(d=\sqrt{(-2+6)^2+(-4 - 3)^2}=\sqrt{(4)^2+(-7)^2}=\sqrt{16 + 49}=\sqrt{65}\approx8.06\) (but we can also note that if we consider the legs as 7 and 4, the distance is \(\sqrt{7^{2}+4^{2}}=\sqrt{49 + 16}=\sqrt{65}\)).

Answer:

Leg 1: \(7\)
Leg 2: \(4\)
Distance: \(\sqrt{65}\) (or approximately \(8.06\))