Question

quiz: directed line segments m(-6, 7) is the midpoint of \\(\overline{df}\\). the coordinates of point d are (-14, 13). what are the coordinates of point f? enter your answer in the boxes

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:
$$x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}$$
Let $D(-14, 13) = (x_1, y_1)$, $F(x, y) = (x_2, y_2)$, and $M(-6, 7) = (x_m, y_m)$.

Step2: Solve for x-coordinate of F

Substitute known values into x-midpoint formula:
$$-6 = \frac{-14 + x}{2}$$
Multiply both sides by 2: $-12 = -14 + x$
Solve for x: $x = -12 + 14 = 2$

Step3: Solve for y-coordinate of F

Substitute known values into y-midpoint formula:
$$7 = \frac{13 + y}{2}$$
Multiply both sides by 2: $14 = 13 + y$
Solve for y: $y = 14 - 13 = 1$

Answer:

$(2, 1)$