Question

calculate the distance between the points $n = (-7,6)$ and $m = (-1,9)$ 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-7,6)$ and $(x_2,y_2)=(-1,9)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-1-(-7)=- 1 + 7 = 6$, $y_2 - y_1=9 - 6=3$.

Step3: Square the differences

$(x_2 - x_1)^2=6^2 = 36$, $(y_2 - y_1)^2=3^2 = 9$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 9=45$.

Step5: Calculate the square - root

$d=\sqrt{45}\approx6.71$ (rounded to the nearest hundredth).

Answer:

$6.71$