Question

find the distance between the points (-2, 9) and (8, 4). round decimals to the nearest tenth. units

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the given points

Let $(x_1,y_1)=(-2,9)$ and $(x_2,y_2)=(8,4)$. Then $x_2 - x_1=8-(-2)=10$ and $y_2 - y_1=4 - 9=-5$.

Step3: Calculate the squares

$(x_2 - x_1)^2=10^2 = 100$ and $(y_2 - y_1)^2=(-5)^2=25$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=100 + 25=125$.

Step5: Calculate the square - root

$d=\sqrt{125}\approx11.2$.

Answer:

$11.2$