Question

If the coordinates of the mid-points of the sides of a triangle are (3, 4) (4, 6) and (5, 7), find its vertices.

Answer 1

The co-ordinates of the midpoint between two points and is given by,

Let the three vertices of the triangle be, and.

The three midpoints are given. Let these points be, and.

Let us now equate these points using the earlier mentioned formula,

Equating the individual components we get,

Using the midpoint of another side we have,

Equating the individual components we get,

Using the midpoint of the last side we have,

Equating the individual components we get,

Adding up all the three equations which have variable ‘x’ alone we have,

Substituting in the above equation we have,

Therefore,

And

Adding up all the three equations which have variable ‘y’ alone we have,

Substituting in the above equation we have,

Therefore,

And

Therefore the co-ordinates of the three vertices of the triangle are.