Question

the midpoint m of $overline{qr}$ has coordinates (1.9, 1.85). point r has coordinates (-10.1, 7.1). 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 $Q(x_1,y_1)$ and $R(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(1.9,1.85)$ and $R(-10.1,7.1)$, let the coordinates of $Q$ be $(x,y)$.

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

We have $\frac{x+( - 10.1)}{2}=1.9$. Multiply both sides by 2: $x - 10.1=1.9\times2 = 3.8$. Then add 10.1 to both sides: $x=3.8 + 10.1=13.9$.

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

We have $\frac{y + 7.1}{2}=1.85$. Multiply both sides by 2: $y+7.1=1.85\times2 = 3.7$. Then subtract 7.1 from both sides: $y=3.7 - 7.1=-3.4$.

Answer:

$(13.9,-3.4)$