Question

the midpoint m of qr has coordinates (1.5, -2.5). point q has coordinates (10, 9). find the coordinates of point r. write the coordinates as decimals or integers. r = ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $Q=(x_1,y_1)=(10,9)$ and $R=(x_2,y_2)$. The mid - point $M=(1.5,-2.5)$.

Step2: Solve for the x - coordinate of R

We know that $\frac{x_1 + x_2}{2}=1.5$. Substitute $x_1 = 10$ into the equation: $\frac{10 + x_2}{2}=1.5$. Multiply both sides by 2: $10+x_2=3$. Then subtract 10 from both sides: $x_2=3 - 10=-7$.

Step3: Solve for the y - coordinate of R

We know that $\frac{y_1 + y_2}{2}=-2.5$. Substitute $y_1 = 9$ into the equation: $\frac{9 + y_2}{2}=-2.5$. Multiply both sides by 2: $9+y_2=-5$. Then subtract 9 from both sides: $y_2=-5 - 9=-14$.

Answer:

$(-7,-14)$