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. (-3,5) and (-5,1) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find difference in x - coordinates

Let $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(-5,1)$. The difference in x - coordinates $\Delta x=x_2 - x_1=-5-(-3)=-2$.

Step2: Find difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=1 - 5=-4$.

Step3: Use distance formula

The distance $d$ between two points is given by the Pythagorean theorem $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x=-2$ and $\Delta y = - 4$ into the formula: $d=\sqrt{(-2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}$.

Step4: Simplify the radical

$\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$.

Answer:

$2\sqrt{5}$