Question

qr has a midpoint at m(12, 3.5). point q is at (20, 0). 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 $Q(x_1,y_1)=(20,0)$ and $R(x_2,y_2)$. The mid - point $M(12,3.5)$.

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

We know that $\frac{x_1 + x_2}{2}=12$. Substitute $x_1 = 20$ into the equation: $\frac{20+x_2}{2}=12$. Multiply both sides by 2: $20 + x_2=24$. Then subtract 20 from both sides: $x_2=24 - 20=4$.

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

We know that $\frac{y_1 + y_2}{2}=3.5$. Substitute $y_1 = 0$ into the equation: $\frac{0 + y_2}{2}=3.5$. Multiply both sides by 2: $y_2=7$.

Answer:

$(4,7)$