Question

cd has a midpoint at m(3, 6). point c is at (5, 4). find the coordinates of point d. write the coordinates as decimals or integers. 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 $C(x_1,y_1)=(5,4)$ and $D(x_2,y_2)$. The mid - point $M(3,6)$.

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

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 5$ and $x_M=3$ into the formula: $\frac{5 + x_2}{2}=3$. Cross - multiply gives $5 + x_2=6$. Then $x_2=6 - 5=1$.

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

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 4$ and $y_M = 6$ into the formula: $\frac{4 + y_2}{2}=6$. Cross - multiply gives $4 + y_2 = 12$. Then $y_2=12 - 4 = 8$.

Answer:

$(1,8)$