Question

the midpoint of the line segment from $p_1$ to $p_2$ is $(-5,4)$. if $p_1 = (-5,3)$, what is $p_2$?
$p_2=square$ (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 $M=(-5,4)$ and $P_1=(-5,3)$, where $x_1=-5,y_1 = 3$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=-5$. Substitute $x_1=-5$ into the equation: $\frac{-5 + x_2}{2}=-5$. Multiply both sides by 2: $-5+x_2=-10$. Add 5 to both sides: $x_2=-5$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=4$. Substitute $y_1 = 3$ into the equation: $\frac{3 + y_2}{2}=4$. Multiply both sides by 2: $3+y_2 = 8$. Subtract 3 from both sides: $y_2=5$.

Answer:

$(-5,5)$