Question

find the distance between the points (-10, -5) and (-4, 9). 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, $(x_1,y_1)=(-10,-5)$ and $(x_2,y_2)=(-4,9)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-4-(-10)=-4 + 10 = 6$, and $y_2 - y_1=9-(-5)=9 + 5 = 14$.

Step3: Square the differences

$(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=14^2 = 196$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 196=232$.

Step5: Calculate the square - root and round

$d=\sqrt{232}\approx15.2$.

Answer:

$15.2$