Question

which methods could you use to calculate the y - coordinate of the midpoint of a vertical line segment with endpoints at (0, 0) and (0, 15)? check all that apply. a. divide 1 by 15. b. divide 15 by 2. c. add the endpoints. d. count by hand.

Explanation:

Step1: Recall mid - point formula

For a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$, the mid - point formula for the $y$ - coordinate is $y=\frac{y_1 + y_2}{2}$. Here, $y_1 = 0$ and $y_2=15$, so $y=\frac{0 + 15}{2}=\frac{15}{2}$.

Step2: Analyze each option

• Option A: Dividing 1 by 15 has no relation to finding the mid - point's $y$ - coordinate, so it's incorrect.
• Option B: Dividing 15 by 2 is equivalent to $\frac{0 + 15}{2}$ using the mid - point formula, so it's correct.
• Option C: Just adding the endpoints ($0+15$) is not the full mid - point formula for the $y$ - coordinate. We need to divide the sum by 2, so it's incorrect.
• Option D: Since the line segment is vertical and the endpoints are simple, we can count by hand. Starting from 0 and going to 15, the mid - point on the $y$ - axis is at 7.5 which can be found by counting, so it's correct.

Answer:

B. Divide 15 by 2., D. Count by hand.