Question

the mid - point m of pq has coordinates (4, 6). point p has coordinates (8, 3). find the coordinates of point q. write the coordinates as decimals or integers. q = ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $M(4,6)$ and $P(8,3)$. Let the coordinates of $Q$ be $(x,y)$.

Step2: Solve for $x$ - coordinate of $Q$

We know that $\frac{8 + x}{2}=4$. Cross - multiply: $8 + x=8$. Then $x=8 - 8=0$.

Step3: Solve for $y$ - coordinate of $Q$

We know that $\frac{3 + y}{2}=6$. Cross - multiply: $3 + y = 12$. Then $y=12 - 3=9$.

Answer:

$(0,9)$