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. (-5,5) and (4,-7) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(-5,5)$ and $(x_2,y_2)=(4, - 7)$.

Step2: Calculate horizontal and vertical distances

The horizontal distance (change in x - values) is $\vert x_2 - x_1\vert=\vert4-(-5)\vert=\vert4 + 5\vert = 9$. The vertical distance (change in y - values) is $\vert y_2 - y_1\vert=\vert-7 - 5\vert=\vert-12\vert = 12$. These are the lengths of the two legs of the right - triangle.

Step3: Apply the Pythagorean theorem

The distance $d$ between two points is given by $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substituting the values, we get $d=\sqrt{(4 + 5)^2+(-7 - 5)^2}=\sqrt{9^2+(-12)^2}=\sqrt{81 + 144}=\sqrt{225}=15$.

Answer:

Leg 1: 9
Leg 2: 12
Hypotenuse: 15