Question

the mid - point m of bc has coordinates (2, 2). point c has coordinates (3, 4). 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 $B$ be $(x,y)$, $M=(2,2)$ and $C=(3,4)$.

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

We know that $\frac{x + 3}{2}=2$. Cross - multiply: $x+3 = 4$. Then $x=4 - 3=1$.

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

We know that $\frac{y + 4}{2}=2$. Cross - multiply: $y + 4=4$. Then $y=4 - 4=0$.

Answer:

$(1,0)$