Question

calculate the distance between the points h = (-7, 8) and p = (-1, 1) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Recall 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, $(x_1,y_1)=(-7,8)$ and $(x_2,y_2)=(-1,1)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-1-(-7)=-1 + 7 = 6$, and $y_2 - y_1=1 - 8=-7$.

Step3: Square the differences

$(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=(-7)^2 = 49$.

Step4: Sum and square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{36 + 49}=\sqrt{85}$.

Answer:

$\sqrt{85}$