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\frac{1}{2} blocks east and 6 blocks north b. 5 blocks east and 4\frac{1}{2} blocks north c. 5 blocks east and 6 blocks north d. 8\frac{1}{2} blocks east and 4\frac{1}{2} blocks north e. 9 blocks east and 7\frac{1}{2} blocks north

Explanation:

Step1: Find the coordinates of B and D

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

Step2: Calculate mid - point of BD

The mid - point formula for 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, $x=\frac{10 + 7}{2}=\frac{17}{2}=8.5$ and $y=\frac{0+3}{2}=1.5$.

Step3: Find the displacement from A

Displacement from A: 8.5 blocks east and 1.5 blocks north of A. But we can also calculate in terms of the overall park structure. The vertical distance from A to the horizontal line of D is 7 blocks. The mid - point's vertical distance from A is $7 - 2.5=4.5$ (since the vertical distance from the top of the park to D is 3 and we are finding mid - point). The horizontal distance from A is 8.5 blocks.

Answer:

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