Question

midpoint
find the midpoint of cd given c(4,1) and d(10,5)
find the midpoint of ab given a(-7,4) and b(3,-4)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Find mid - point of CD

For points $C(4,1)$ and $D(10,5)$, $x_1 = 4$, $y_1 = 1$, $x_2 = 10$, $y_2 = 5$.
$x$ - coordinate of mid - point: $\frac{4 + 10}{2}=\frac{14}{2}=7$
$y$ - coordinate of mid - point: $\frac{1+5}{2}=\frac{6}{2}=3$
The mid - point of $CD$ is $(7,3)$.

Step3: Find mid - point of AB

For points $A(-7,4)$ and $B(3,-4)$, $x_1=-7$, $y_1 = 4$, $x_2 = 3$, $y_2=-4$.
$x$ - coordinate of mid - point: $\frac{-7 + 3}{2}=\frac{-4}{2}=-2$
$y$ - coordinate of mid - point: $\frac{4+( - 4)}{2}=\frac{4 - 4}{2}=0$
The mid - point of $AB$ is $(-2,0)$.

Answer:

Mid - point of $CD$ is $(7,3)$; Mid - point of $AB$ is $(-2,0)$