HOW TO FIND THE VERTICES OF A TRIANGLE IF THE MIDPOINTS ARE GIVEN

Example 1 :

The mid-points of the sides of a triangle are (5, 1), (3, -5) and (-5, -1). Find the coordinates of the vertices of the triangle. 

Solution :

Let D, E and F be the mid points of the sides AB, BC and CA of ΔABC.

D(x₁, y₁) = (5, 1)

E(x₂, y₂) = (3, -5)

F(x₃, y₃) = (-5, -1)

Vertex A :

A(x₁ + x₃ - x_2, y₁ + y₃ - y₂)

A(5 - 5 - 3, 1 - 1 - (-5))

A(-3, 5)

Vertex B :

B(x₁ + x₂ - x_3, y₁ + y₂ - y₃)

B(5 + 3 - (-5), 1 - 5 - (-1))

B(8 + 5, 1 - 5 + 1)

B(13, -3)

Vertex C :

C(x₂ + x₃ - x_1, y₂ + y₃ - y₁)

C(3 - 5 - 5, -5 - 1 - 1)

C(3 - 10, -5 - 2)

C(-7, -7)

Example 2 :

The mid-points of the sides of a triangle are (5, 3), (4, 0) and (2, 2). Find the coordinates of the vertices of the triangle. 

Solution :

Let D, E and F be the mid points of the sides AB, BC and CA of ΔABC.

D(x₁, y₁) = (5, 3)

E(x₂, y₂) = (4, 0)

F(x₃, y₃) = (2, 2)

Vertex A :

A(x₁ + x₃ - x_2, y₁ + y₃ - y₂)

A(5 + 2 - 4, 3 + 2 - 0)

A(3, 5)

Vertex B :

B(x₁ + x₂ - x_3, y₁ + y₂ - y₃)

B(5 + 4 - 2, 3 + 0 - 2)

B(7, 1)

Vertex C :

C(x₂ + x₃ - x_1, y₂ + y₃ - y₁)

C(4 + 2 - 5, 0 + 2 - 3)

C(1, -1)

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.