Question

the mid - point m of bc has coordinates (-46.5, -18). point b has coordinates (-93, 58). find the coordinates of point c. write the coordinates as decimals or integers.

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 $B=(x_1,y_1)=(-93,58)$ and the coordinates of point $C=(x_2,y_2)$. The mid - point $M=(-46.5,-18)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1=-93$ and $x_M = - 46.5$, we get $\frac{-93+x_2}{2}=-46.5$. Multiply both sides by 2: $-93 + x_2=-46.5\times2=-93$. Then $x_2=-93 + 93=0$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 58$ and $y_M=-18$, we get $\frac{58+y_2}{2}=-18$. Multiply both sides by 2: $58+y_2=-18\times2=-36$. Then $y_2=-36 - 58=-94$.

Answer:

$(0,-94)$