Question

select the correct answer. gradys father is building a 15 - meter fence with the start of the fence at coordinates (8, 5) and the midpoint of the fence at coordinates (3.5, -1). what are the coordinates of the other end of the fence? (-15, -3) (12, 6) (2, -9) (-1, -7)

Explanation:

Step1: Recall midpoint formula

The midpoint $M(x_m, y_m)$ of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$$x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}$$
We know $(x_1, y_1)=(8,5)$, $(x_m, y_m)=(3.5,-1)$, and solve for $(x_2, y_2)$.

Step2: Solve for $x_2$

Rearrange the x-midpoint formula to isolate $x_2$:
$$x_2 = 2x_m - x_1$$
Substitute values:
$$x_2 = 2(3.5) - 8 = 7 - 8 = -1$$

Step3: Solve for $y_2$

Rearrange the y-midpoint formula to isolate $y_2$:
$$y_2 = 2y_m - y_1$$
Substitute values:
$$y_2 = 2(-1) - 5 = -2 - 5 = -7$$

Answer:

(-1,-7)