Question

the midpoint m of $overline{pq}$ has coordinates (5, -7). point q has coordinates (5, -1). find the coordinates of point p. write the coordinates as decimals or integers. p = ( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(5,-7)$ and $Q(5,-1)$, let the coordinates of $P$ be $(x,y)$.

Step2: Solve for the x - coordinate of P

We know that $\frac{x + 5}{2}=5$. Multiply both sides by 2: $x + 5=10$. Then subtract 5 from both sides: $x=10 - 5=5$.

Step3: Solve for the y - coordinate of P

We know that $\frac{y+( - 1)}{2}=-7$. Multiply both sides by 2: $y - 1=-14$. Then add 1 to both sides: $y=-14 + 1=-13$.

Answer:

$(5,-13)$