Questions: 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 park's borders run east-west or northsouth.) 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

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 park's borders run east-west or northsouth.) 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

Transcript text: 21. 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 park's borders run east-west or northsouth.) 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

Solution

Solution Steps

Step 1: Find the coordinates of B and D.

Taking A as the origin (0,0), the coordinates of B are (10, 0) and the coordinates of D are (10, 12-3) = (10,9).

Step 2: Find the midpoint between B and D.

The midpoint M between two points (x1, y1) and (x2, y2) is given by ((x1+x2)/2, (y1+y2)/2). Therefore, the midpoint between B(10,0) and D(10,9) is ((10+10)/2, (0+9)/2) = (10, 4.5).

Step 3: Interpret the coordinates of the midpoint.

The coordinates of the midpoint (10, 4.5) mean that the fountain is 10 blocks east and 4.5 blocks north of point A.

Final Answer

B. 5 blocks east and $4 \frac{1}{2}$ blocks north is incorrect. The correct answer is C. 10 blocks east and 4.5 blocks north. The given options do not contain the correct answer.

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