Question

find the coordinates of the missing endpoint if b is the mid - point of $overline{ac}$. a(2, 1), b(10, 4)

Explanation:

Step1: Use mid - point formula.

Let the coordinates of $C$ be $(x,y)$. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1 = 2,y_1 = 1$ (coordinates of $A$), and the mid - point $B(10,4)$. So $\frac{2 + x}{2}=10$ and $\frac{1 + y}{2}=4$.

Step2: Solve for $x$.

$2 + x=20$, so $x = 18$.

Step3: Solve for $y$.

$1 + y = 8$, so $y = 7$.

Answer:

$(18,7)$