Question

calculate the distance between the points l=(6, 0) and h=(-2, 7) in the coordinate plane. give an exact answer (not a decimal approximation). distance:

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(6,0)$ and $(x_2,y_2)=(-2,7)$. Then $x_2 - x_1=-2 - 6=-8$ and $y_2 - y_1=7 - 0 = 7$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-8)^2 = 64$ and $(y_2 - y_1)^2=7^2 = 49$.

Step4: Sum squares and find square - root

$d=\sqrt{64 + 49}=\sqrt{113}$.

Answer:

$\sqrt{113}$