Question

the midpoint of the line segment from p1 to p2 is (-2,1). if p1 = (-5,6), what is p2?
p2 = □ (type an ordered pair.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $P_1=(x_1,y_1)$ and $P_2=(x_2,y_2)$ is $M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M=(-2,1)$ and $P_1=(-5,6)$, we have $\frac{x_1 + x_2}{2}=-2$ and $\frac{y_1 + y_2}{2}=1$.

Step2: Solve for $x_2$

Substitute $x_1=-5$ into $\frac{x_1 + x_2}{2}=-2$. We get $\frac{-5 + x_2}{2}=-2$. Multiply both sides by 2: $-5 + x_2=-4$. Then add 5 to both sides: $x_2=-4 + 5=1$.

Step3: Solve for $y_2$

Substitute $y_1 = 6$ into $\frac{y_1 + y_2}{2}=1$. We get $\frac{6 + y_2}{2}=1$. Multiply both sides by 2: $6 + y_2=2$. Then subtract 6 from both sides: $y_2=2 - 6=-4$.

Answer:

$(1,-4)$