Question

given m is the midpoint of cd, find the coordinates of the other endpoint. m(4, 2) and c(6, 5)

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 $C(x_1,y_1)=(6,5)$ and $D(x_2,y_2)$ and $M(4,2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 6$ and $x_M=4$ into the formula: $\frac{6 + x_2}{2}=4$. Multiply both sides by 2: $6 + x_2=8$. Then subtract 6 from both sides: $x_2=8 - 6=2$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 5$ and $y_M = 2$ into the formula: $\frac{5 + y_2}{2}=2$. Multiply both sides by 2: $5 + y_2=4$. Then subtract 5 from both sides: $y_2=4 - 5=-1$.

Answer:

$(2,-1)$