Question

a park has the shape and dimensions in blocks given below. a water fountain is located halfway between point b and point d. which of the following is the location of the water fountain from point a? (note: the parks borders run east - west or north - south.) a. 3 1/2 blocks east and 6 blocks north b. 5 blocks east and 4 1/2 blocks north c. 5 blocks east and 6 blocks north d. 8 1/2 blocks east and 4 1/2 blocks north e. 9 blocks east and 7 1/2 blocks north

Explanation:

Step1: Find coordinates of B and D

Let A be the origin (0, 0). Then B has coordinates (10, 0) (10 blocks east of A). D has coordinates (7, 3) (7 blocks east and 3 blocks north of A).

Step2: Use mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1=10,y_1 = 0,x_2=7,y_2 = 3$. So the mid - point (location of water fountain) has $x=\frac{10 + 7}{2}=\frac{17}{2}=8.5$ and $y=\frac{0+3}{2}=1.5$.

Step3: Find distance from A

The distance from A(0, 0) to the water - fountain is 8.5 blocks east and 1.5 + 3=4.5 blocks north.

Answer:

D. $8\frac{1}{2}$ blocks east and $4\frac{1}{2}$ blocks north