Question

pq has a mid - point at m(2, 9). point q is at (0, 8). 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $P=(x,y)$ and $Q=(0,8)$ and $M=(2,9)$.

Step2: Solve for the x - coordinate of P

We know that $\frac{x + 0}{2}=2$. Cross - multiply to get $x+0 = 4$, so $x = 4$.

Step3: Solve for the y - coordinate of P

We know that $\frac{y + 8}{2}=9$. Cross - multiply: $y + 8=18$. Then subtract 8 from both sides: $y=18 - 8=10$.

Answer:

$(4,10)$