Question

the midpoint of the line segment from $p_1$ to $p_2$ is $(-2,9)$. if $p_1 = (-3,9)$, what is $p_2$?
$p_2 = \square$ (type an ordered pair.)

Explanation:

Step1: Recall midpoint formula

The midpoint $M=(x_m,y_m)$ of a segment with endpoints $P_1=(x_1,y_1)$ and $P_2=(x_2,y_2)$ is given by:
$$x_m=\frac{x_1+x_2}{2}, \quad y_m=\frac{y_1+y_2}{2}$$

Step2: Solve for $x_2$

Substitute $x_m=-2$, $x_1=-3$ into the x-coordinate formula:
$$-2=\frac{-3+x_2}{2}$$
Multiply both sides by 2: $-4=-3+x_2$
Solve for $x_2$: $x_2=-4+3=-1$

Step3: Solve for $y_2$

Substitute $y_m=9$, $y_1=9$ into the y-coordinate formula:
$$9=\frac{9+y_2}{2}$$
Multiply both sides by 2: $18=9+y_2$
Solve for $y_2$: $y_2=18-9=9$

Answer:

$(-1, 9)$