Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-6,0) and (-1,4)

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, $x_1=-6,y_1 = 0,x_2=-1,y_2 = 4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-1-(-6)=-1 + 6=5$ and $y_2 - y_1=4 - 0 = 4$.

Step3: Square the differences and sum

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=4^2 = 16$. Then $(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 16=41$.

Step4: Calculate the distance

$d=\sqrt{41}\approx6.4$.

Answer:

$6.4$