Question

the mid - point of the line segment from p1 to p2 is (-5,4). if p1 = (-6,9), 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 $M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $P_1=(-6,9)$ and $M=(-5,4)$, and we want to find $P_2=(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1=-6$ and $x_M = - 5$ into the formula:
$\frac{-6 + x_2}{2}=-5$. Multiply both sides by 2: $-6+x_2=-10$. Then add 6 to both sides: $x_2=-10 + 6=-4$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 9$ and $y_M=4$ into the formula:
$\frac{9 + y_2}{2}=4$. Multiply both sides by 2: $9 + y_2=8$. Then subtract 9 from both sides: $y_2=8 - 9=-1$.

Answer:

$(-4,-1)$