Question

map on the right to answer the following questions. how far must you travel in order to go to the skate park from your home? 2. after school, jerry headed to the library to study for a few hours. he then went to the skate park to hang out with friends before he went home for the night. how far did jerry walk after school let out? 3. jerry’s older sister, cheryl, wants to pick him up halfway between the skate park and his house. what are the coordinates of this pick - up point? 4. how far must cheryl drive in order to pick up jerry at the pick - up point?

Explanation:

1.

Step1: Assume home is at point $(x_1,y_1)$ and skate - park is at point $(x_2,y_2)$. Let's assume home is at $(5,5)$ and skate - park is at $(- 3,1)$. Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

$d=\sqrt{(-3 - 5)^2+(1 - 5)^2}$

Step2: Calculate the values inside the square - root.

$(-3 - 5)^2=(-8)^2 = 64$ and $(1 - 5)^2=(-4)^2 = 16$.
$d=\sqrt{64 + 16}$

Step3: Add the values inside the square - root and then find the square root.

$d=\sqrt{80}=4\sqrt{5}\approx8.94$

Step1: Assume school is at point $(x_{s},y_{s})=(5,2)$, library is at point $(x_{l},y_{l})=(0,3)$ and skate - park is at point $(x_{p},y_{p})=(-3,1)$. First, find the distance from school to library using the distance formula $d_1=\sqrt{(x_{l}-x_{s})^2+(y_{l}-y_{s})^2}$.

$d_1=\sqrt{(0 - 5)^2+(3 - 2)^2}=\sqrt{(-5)^2+1^2}=\sqrt{25 + 1}=\sqrt{26}$

Step2: Then find the distance from library to skate - park using the distance formula $d_2=\sqrt{(x_{p}-x_{l})^2+(y_{p}-y_{l})^2}$.

$d_2=\sqrt{(-3 - 0)^2+(1 - 3)^2}=\sqrt{(-3)^2+(-2)^2}=\sqrt{9 + 4}=\sqrt{13}$

Step3: The total distance $D=d_1 + d_2$.

$D=\sqrt{26}+\sqrt{13}\approx5.1+3.6 = 8.7$

Step1: Use the mid - point formula. If the skate - park is at $(x_1,y_1)=(-3,1)$ and home is at $(x_2,y_2)=(5,5)$. The mid - point formula is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

$x=\frac{-3 + 5}{2}=1$
$y=\frac{1+5}{2}=3$

Answer:

$4\sqrt{5}\approx8.94$

2.