Question

calculate the distance between the points m = (-9, 9) and p = (-5, 2) in the coordinate plane. round your answer to the nearest hundredth.

Explanation:

Step1: Identify the 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 $M(-9,9)$ and $P(-5,2)$, $x_1=-9,y_1 = 9,x_2=-5,y_2 = 2$.

Step2: Calculate the differences

$x_2 - x_1=-5-(-9)=-5 + 9=4$ and $y_2 - y_1=2 - 9=-7$.

Step3: Square the differences

$(x_2 - x_1)^2=4^2 = 16$ and $(y_2 - y_1)^2=(-7)^2 = 49$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 49=65$.

Step5: Calculate the square - root

$d=\sqrt{65}\approx 8.06$.

Answer:

$8.06$