Question

Find the coordinates of the missing endpoint if B is the midpoint of AC. C(5/3,-6),B(8/3,4)

Answer 1

Given :

$C(\dfrac{5}{3},-6)\ , \ B(\dfrac{8}{3},4)$ .

B is the mid-point of AC .

To Find :

The missing endpoint if B is the midpoint of AC.

Solution :

Let , coordinate of point A is ( h, k) .

So , mid-point B is given by :

$(\dfrac{\dfrac{5}{3}+h}{2},\dfrac{-6+k}{2})$

Comparing above point with $B(\dfrac{8}{3},4)$ , we get :

$\dfrac{\dfrac{5}{3}+h}{2}=\dfrac{8}{3}\\\\h+\dfrac{5}{3}=\dfrac{16}{3}\\\\h=\dfrac{11}{3}$        $\dfrac{-6+k}{2}=4\\\\k=14$

Therefore , the value of point A is $(\dfrac{11}{3},14)$ .

Hence , this is the required solution .