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, -1) and (-8, -4) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(-5,-1)$ and $(x_2,y_2)=(-8,-4)$.

Step2: Calculate horizontal and vertical distances

The horizontal distance $\Delta x=x_2 - x_1=-8-(-5)=- 3$. The vertical distance $\Delta y=y_2 - y_1=-4-(-1)=-3$.

Step3: Apply distance formula

The distance $d$ between two points is given by the Pythagorean - like formula $d = \sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x=-3$ and $\Delta y = - 3$ into the formula: $d=\sqrt{(-3)^2+(-3)^2}=\sqrt{9 + 9}=\sqrt{18}$.

Step4: Simplify the radical

$\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$.

Answer:

$3\sqrt{2}$