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: Find horizontal side length

Find the difference in x - coordinates. Let $(x_1,y_1)=(-5,5)$ and $(x_2,y_2)=(4, - 7)$. The difference in x - coordinates $\Delta x=x_2 - x_1=4-(-5)=9$.

Step2: Find vertical side length

Find the difference in y - coordinates. The difference in y - coordinates $\Delta y=y_2 - y_1=-7 - 5=-12$.

Step3: Use Pythagorean theorem

The distance $d$ between the two points (length of the hypotenuse) is given by $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x = 9$ and $\Delta y=-12$ into the formula: $d=\sqrt{9^{2}+(-12)^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$.

Answer:

$15$