Question

the midpoint m of $overline{bc}$ has coordinates (13.5, 5). point c has coordinates (14, 15). find the coordinates of point b. write the coordinates as decimals or integers. b = ( , )

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 the coordinates of point $B$ be $(x,y)$ and point $C(14,15)$ and mid - point $M(13.5,5)$.

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

We know that $\frac{x + 14}{2}=13.5$. Multiply both sides by 2: $x + 14=27$. Then subtract 14 from both sides: $x=27 - 14=13$.

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

We know that $\frac{y + 15}{2}=5$. Multiply both sides by 2: $y + 15 = 10$. Then subtract 15 from both sides: $y=10 - 15=-5$.

Answer:

$(13,-5)$