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

Explanation:

Step1: Find difference in x - coordinates

Let $(x_1,y_1)=(8, - 7)$ and $(x_2,y_2)=(-1,-4)$. The difference in x - coordinates $\Delta x=x_2 - x_1=-1 - 8=-9$.

Step2: Find difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=-4-(-7)=-4 + 7 = 3$.

Step3: Apply distance formula

The distance $d$ between two points is given by the distance formula $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$. Substitute $\Delta x=-9$ and $\Delta y = 3$ into the formula: $d=\sqrt{(-9)^2+3^2}=\sqrt{81 + 9}=\sqrt{90}$.

Step4: Simplify the radical

We can simplify $\sqrt{90}=\sqrt{9\times10}=3\sqrt{10}$.

Answer:

$3\sqrt{10}$