Question

The midpoint of AB is M (5, 6). If the coordinates of A are (3, 8), what are the

coordinates of B?

Answer 1

(7, 4)

Explanation:

`\text{Let the coordinates of B } = x_(B) , y_(B) \\\text{Let the coordinates of A} = x_(A) , y_(A) \\\text{Let the coordinates of midpoint M} = x_(M) , y_(M)`

By the midpoint formula,

`(x_(M),y_(M)) = ((x_(A) + x_(B))/(2) , (y_(A) + y_(B))/(2) )`

`x_(M) = (x_(A) + x_(B))/(2) \\y_(M) = (y_(A) + y_(B))/(2) \\`

We have coordinates of midpoint as (5, 6) and coordinates of A as (3,8)
So

`5 = (3 + x_(B))/(2) \\\\\\textrm{Cross-multiplying } 10 = 3 + x_(B)} \textrm{ or } x_(B) = 10-3 = 7\\`

`6 = (8 + y_(B))/(2) \\\\\\\\textrm{Cross-multiplying } 12 = 8 + y_(B)} \textrm{ or } y_(B) = 12-8 = 4\\`

So coordinates of B are (7,4)