Question

The midpoint of AB is M(3, -1). If the coordinates of A are (5,1), what are the

coordinates of B?

Answer 1

Given parameters:

Midpoint of AB = M(3, -1)

Coordinates of A = (5,1)

Unknown:

Coordinates of B = ?

Solution:

To find the mid point of any line, we use the expression below;

`x_(m) = (x_(1) + x_(2) )/(2)` and
`y_(m) = (y_(1) + y_(2) )/(2)`

where
`x_(m)` and
`y_(m)` = coordinates of the mid points = 3 and -1

x₁ = 5 and y₁ = 1

x₂ = ? and y₂ = ?

Now let us input the variables and solve,

3 =
`(5 + x_(2) )/(2)` and -1 =
`(1 + y_(2) )/(2)`

5 + x₂ = 6 -2 = 1 + y₂

x₂ = 1 y₂ = -2 -1 = -3

The coordinates of B = 1, -3