Question

1. find the distance between the two points rounding to the nearest tenth if necessary. (-6,2) and (-4,8)

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, $(x_1,y_1)=(-6,2)$ and $(x_2,y_2)=(-4,8)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-4-(-6)=-4 + 6=2$, $y_2 - y_1=8 - 2 = 6$.

Step3: Square the differences

Square the results from step 2. $(x_2 - x_1)^2=2^2 = 4$, $(y_2 - y_1)^2=6^2=36$.

Step4: Sum the squared - differences

Add the squared differences: $(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 36=40$.

Step5: Calculate the distance

Take the square - root of the sum: $d=\sqrt{40}\approx6.3$.

Answer:

$6.3$