Question

find the distance between the points (-5, 5) and (1, -3). round decimals to the nearest tenth.

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, $(x_1,y_1)=(-5,5)$ and $(x_2,y_2)=(1, - 3)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=1-(-5)=6$ and $y_2 - y_1=-3 - 5=-8$.

Step3: Square the differences

Square the results from Step 2. $(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=(-8)^2 = 64$.

Step4: Sum the squared differences

Add the squared - differences: $(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Calculate the square - root

Take the square - root of the sum: $d=\sqrt{100}=10$.

Answer:

10