Question

pq has a midpoint at m(11.5, 11). point p is at (3, 6). find the coordinates of point q. write the coordinates as decimals or integers. q = ( , )

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 $M(11.5,11)$ and $P(3,6)$, let the coordinates of $Q$ be $(x,y)$. Then $\frac{3 + x}{2}=11.5$ and $\frac{6 + y}{2}=11$.

Step2: Solve for $x$

Solve the equation $\frac{3 + x}{2}=11.5$. Multiply both sides by 2: $3 + x=11.5\times2 = 23$. Then subtract 3 from both sides: $x=23 - 3=20$.

Step3: Solve for $y$

Solve the equation $\frac{6 + y}{2}=11$. Multiply both sides by 2: $6 + y=11\times2 = 22$. Then subtract 6 from both sides: $y=22 - 6 = 16$.

Answer:

$(20,16)$