Question

calculate the distance between the points m=(6, 0) and p=(-2, 7) in the coordinate plane. round your answer to the nearest hundredth.

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

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 49=113$.

Step5: Calculate distance

$d=\sqrt{113}\approx10.63$.

Answer:

$10.63$