Question

find the distance between the points (-7, -4) and (10, 7). round decimals to the nearest tenth. units

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, $(x_1,y_1)=(-7,-4)$ and $(x_2,y_2)=(10,7)$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=10-(-7)=10 + 7=17$.
$y_2 - y_1=7-(-4)=7 + 4=11$.

Step3: Square the differences and sum them

$(x_2 - x_1)^2=17^2 = 289$ and $(y_2 - y_1)^2=11^2 = 121$.
The sum is $289+121 = 410$.

Step4: Calculate the distance

$d=\sqrt{410}\approx20.2$.

Answer:

$20.2$