Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points, to the nearest tenth (if necessary). (5, -9) and (8, -3) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find horizontal distance

The horizontal distance (difference in x - coordinates) between the points $(x_1,y_1)=(5, - 9)$ and $(x_2,y_2)=(8,-3)$ is $\Delta x=x_2 - x_1$.
$\Delta x=8 - 5=3$

Step2: Find vertical distance

The vertical distance (difference in y - coordinates) between the points is $\Delta y=y_2 - y_1$.
$\Delta y=-3-( - 9)=-3 + 9 = 6$

Step3: Use Pythagorean theorem

The distance $d$ between two points is given by the Pythagorean theorem $d=\sqrt{(\Delta x)^2+(\Delta y)^2}$.
$d=\sqrt{3^2+6^2}=\sqrt{9 + 36}=\sqrt{45}\approx6.7$

Answer:

$6.7$