Question

1. m is the midpoint of $overline{pq}$. p has coordinates $(-1, 5)$ and m has coordinates $(-3, 2)$. what are the coordinates of q?

a. $(-4, -22)$
b. $(-2, -5.5)$
c. $(-5, -1)$
d. $(-6, -12)$

Explanation:

Step1: Recall midpoint formula

The midpoint $M(x_m, y_m)$ of a segment with endpoints $P(x_p, y_p)$ and $Q(x_q, y_q)$ is given by:
$$x_m = \frac{x_p + x_q}{2}, \quad y_m = \frac{y_p + y_q}{2}$$

Step2: Solve for $x_q$

Substitute $x_m=-3$, $x_p=-1$ into the x-coordinate formula:
$$-3 = \frac{-1 + x_q}{2}$$
Multiply both sides by 2: $-6 = -1 + x_q$
Solve for $x_q$: $x_q = -6 + 1 = -5$

Step3: Solve for $y_q$

Substitute $y_m=2$, $y_p=5$ into the y-coordinate formula:
$$2 = \frac{5 + y_q}{2}$$
Multiply both sides by 2: $4 = 5 + y_q$
Solve for $y_q$: $y_q = 4 - 5 = -1$

Answer:

c. (-5, -1)