Midpoint Theorem Triangle

Introduction:

The triangle is a closed plane and it has three straight lines. Those lines are meeting at three different points. The intersection point of the triangle is called as vertices of the triangle. There are three vertices in the triangle. And it is congruent to one half of the third side of the triangle. The triangle midpoints are denoted as (D, E, and F).


Mid-point theorem:

Midpoint formula for the triangle is,

  ((x1 + x2) / 2), ((y1 +y2) / 2).

Here, x1 and y1 - coordinates of first vertices.

  x2 and y2 - coordinates of second vertices.

  (x1 + x2) / 2 = mid-point of x-co-ordinates

  (y1 + y2) / 2 = mid-point of y-co-ordinates

Example 1:

  Find out the midpoint of triangle points (1,2), (3,8). Using the mid-point theorem of triangle.

Solution:

  Midpoint formula for triangle = ((x1 + x2) / 2, (y1 + y2) / 2).

  Here, x1 = 1, x2 = 3 and y1 = 2, y2 = 8.

  Therefore,   

  Midpoint = ((1 + 3) / 2, (2 + 8) / 2)

  = (4 / 2, 10 / 2)

  = (2, 5).

Example 2:

  Find mid-point of the given triangle by using mid-point theorem.

Solution:


Midpoint of AB = D

  D = (2 + 4) / 2, (4 + 1) / 2

  D = 3, 5 / 2

  Midpoint of BC = E

  E = (4 + 1) / 2, (1 + 3) / 2

  E = 5 /  2, 2

  Mid-point of AC = F

  F = (2 + 1) / 2, (4 + 3) / 2

  F = 3 / 2, 7 / 2

Answer:

  Mid-point of, AB = 3, 5 / 2

  BC = 5 /  2, 2

  AC = 3 / 2, 7 / 2


Practice problem:

1) Find the mid-point of the triangle using mid-point theorem with points (4, 8) and (6, 12)

2) Find the mid-point of the triangle using mid-point theorem with points (12, 2) and (5, 14)

3) Find the mid-point of the triangle using mid-point theorem with points (22, 4) and (10, 21)

Answer:

 1. (5, 10)

2. (8.5, 8)

3. (16, 12.5)