Question

karen is planning a park for her neighborhood, and she wants to incorporate various features in the space. shes using mathematical concepts to plan the layout efficiently. karen wants to create a path that connecting the sandbox and the swings in the park. she needs to determine the length of the path. calculate the distance between the sandbox at (-8,2) and the swings at (3,10). round your answer to the nearest whole number. answer attempt 1 out of 2 9 13 14 16

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, $(x_1,y_1)=(-8,2)$ and $(x_2,y_2)=(3,10)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=3-(-8)=3 + 8=11$, $y_2 - y_1=10 - 2 = 8$.

Step3: Square the differences

$(x_2 - x_1)^2=11^2 = 121$ and $(y_2 - y_1)^2=8^2=64$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=121+64 = 185$.

Step5: Calculate the square - root

$d=\sqrt{185}\approx13.6$.

Step6: Round to the nearest whole number

Rounding $13.6$ to the nearest whole number gives $14$.

Answer:

14