Question

find the distance between the points (11, 5) and (2, 11). 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, $x_1 = 11$, $y_1 = 5$, $x_2 = 2$, $y_2 = 10$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=2 - 11=-9$ and $y_2 - y_1 = 10 - 5 = 5$.

Step3: Square the differences

$(x_2 - x_1)^2=(-9)^2 = 81$ and $(y_2 - y_1)^2=5^2 = 25$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 25=106$.

Step5: Calculate the square - root

$d=\sqrt{106}\approx10.3$.

Answer:

$10.3$