Question

select the coordinates of the missing endpoint if b is the midpoint of $overline{ac}$. $c(\frac{5}{3}, - 6), b(\frac{8}{3},4)$

o a) $a(\frac{2}{3},6)$
o b) $a(\frac{11}{3},14)$
o c) $a(\frac{5}{3},14)$
o d) $a(\frac{2}{3},7)$

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $A(x_1,y_1)$ and $C(x_2,y_2)$ with mid - point $B(x_m,y_m)$ is $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$. Let $A(x,y)$, $C(\frac{5}{3},-6)$ and $B(\frac{8}{3},4)$.

Step2: Solve for x - coordinate of A

We have $\frac{8}{3}=\frac{x+\frac{5}{3}}{2}$. Cross - multiply: $2\times\frac{8}{3}=x+\frac{5}{3}$, so $\frac{16}{3}=x+\frac{5}{3}$. Then $x=\frac{16}{3}-\frac{5}{3}=\frac{16 - 5}{3}=\frac{11}{3}$.

Step3: Solve for y - coordinate of A

We have $4=\frac{y+( - 6)}{2}$. Cross - multiply: $2\times4=y - 6$, so $8=y - 6$. Then $y=8 + 6=14$.

Answer:

B. $A(\frac{11}{3},14)$