Question

calculate the distance between the points k=(8, 0) and j=(5, - 4) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, for points $K=(8,0)$ and $J=(5, - 4)$, $x_1 = 8,y_1 = 0,x_2 = 5,y_2=-4$.

Step2: Substitute values

$d=\sqrt{(5 - 8)^2+(-4 - 0)^2}=\sqrt{(-3)^2+(-4)^2}$.

Step3: Calculate squares

$(-3)^2=9$ and $(-4)^2 = 16$, so $d=\sqrt{9 + 16}$.

Step4: Add and simplify

$9+16 = 25$, so $d=\sqrt{25}=5$.

Answer:

$5$