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((5)/(3),-6)\ , \ B((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 :

`(((5)/(3)+h)/(2),(-6+k)/(2))`

Comparing above point with
`B((8)/(3),4)` , we get :

`((5)/(3)+h)/(2)=(8)/(3)\\\\h+(5)/(3)=(16)/(3)\\\\h=(11)/(3)`
`(-6+k)/(2)=4\\\\k=14`

Therefore , the value of point A is
`((11)/(3),14)` .

Hence , this is the required solution .