Question

biking rhea is using a coordinate grid to map out how far she biked from each place in town. if each unit on the grid represents 1 kilometer, the distance rhea traveled from point k to point l to point m is km. round to the nearest kilometer, if necessary.

Explanation:

Step1: Recall distance formula

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

Step2: Calculate distance from K(2,2) to L(-1,6)

Let $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(-1,6)$. Then $d_{KL}=\sqrt{(-1 - 2)^2+(6 - 2)^2}=\sqrt{(-3)^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step3: Calculate distance from L(-1,6) to M(-4,2)

Let $(x_1,y_1)=(-1,6)$ and $(x_2,y_2)=(-4,2)$. Then $d_{LM}=\sqrt{(-4+1)^2+(2 - 6)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step4: Calculate total distance

The total distance from K to L to M is $d=d_{KL}+d_{LM}=5 + 5=10$.

Answer:

10