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. (-7, -8) and (-4, -3)

Explanation:

Step1: Find the difference in x - coordinates

Let $(x_1,y_1)=(-7,-8)$ and $(x_2,y_2)=(-4,-3)$. The difference in x - coordinates $\Delta x=x_2 - x_1=-4-(-7)=3$.

Step2: Find the difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=-3-(-8)=5$.

Step3: Use the Pythagorean theorem

The lengths of the legs of the right - triangle are the absolute values of $\Delta x$ and $\Delta y$. The distance $d$ between the two points (the length of the hypotenuse) is given by the Pythagorean theorem $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x = 3$ and $\Delta y = 5$ into the formula: $d=\sqrt{3^2 + 5^2}=\sqrt{9 + 25}=\sqrt{34}$.

Answer:

Leg 1: 3
Leg 2: 5
Hypotenuse: $\sqrt{34}$