Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar. the coordinates of c are (4,4), and the mid - point of cd is at m(-2,-6). what are the coordinates of point d? d( , )

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 $C(x_1,y_1)=(4,4)$ and $D(x_2,y_2)$. The mid - point $M(-2,-6)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-2$. Substitute $x_1 = 4$ into the equation: $\frac{4+x_2}{2}=-2$. Multiply both sides by 2: $4 + x_2=-4$. Then subtract 4 from both sides: $x_2=-4 - 4=-8$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-6$. Substitute $y_1 = 4$ into the equation: $\frac{4+y_2}{2}=-6$. Multiply both sides by 2: $4 + y_2=-12$. Then subtract 4 from both sides: $y_2=-12 - 4=-16$.

Answer:

$(-8,-16)$