Question

1. you and your cousin are planning to go to an amusement park. the amusement park is 36 miles north of your house. your cousin lives 15 miles east of your house. how far away from the amusement park does your cousin live? use the coordinate plane below to draw the diagram that represents this situation. then, find the distance.

Explanation:

Step1: Assign coordinates to locations

Let your house = $(0,0)$.
Cousin's house: $(15,0)$ (15 miles east).
Amusement park: $(0,36)$ (36 miles north of your house).

Step2: Apply distance formula

Distance between $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Substitute $(15,0)$ and $(0,36)$:
$\sqrt{(0-15)^2+(36-0)^2} = \sqrt{(-15)^2+36^2}$

Step3: Calculate squared terms

$\sqrt{225 + 1296}$

Step4: Sum and simplify root

$\sqrt{1521} = 39$

Answer:

39 miles

(Note: To represent this on the coordinate plane: plot your house at the origin, cousin's house 15 units right on the x-axis, amusement park 36 units up on the y-axis, then draw a line connecting the cousin's house to the amusement park.)