Question

find the distance between the points (-9, 1) and (-2, 10). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(-9,1)$ and $(x_2,y_2)=(-2,10)$. Then $x_2 - x_1=-2-(-9)=7$ and $y_2 - y_1=10 - 1 = 9$.

Step3: Calculate squares

$(x_2 - x_1)^2=7^2 = 49$ and $(y_2 - y_1)^2=9^2=81$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 81=130$.

Step5: Find square - root

$d=\sqrt{130}\approx11.4$.

Answer:

$11.4$