PRACTICAL PROBLEMS USING MIDPOINT FORMULA

Practical Problems Using Midpoint Formula

Here we are going to see some example problems using the concept of midpoint.

Practical Problems Using Midpoint Formula

Question 1 :

The points A(−3, 6) , B(0, 7) and C(1, 9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallelogram

Solution :

In order to prove ABCD is a parallelogram, we have to find the point D.

  =  D (-3+1-0, 6+9-7)

  =  D (-2, 8)

In ABCD is a parallelogram, then midpoint of diagonals AC and BD will be equal.

Midpoint of AC  =  (-3 + 1)/2, (6 + 9)/2

  =  -2/2, 15/2

  =  (-1, 15/2)

Midpoint of BD

B(0, 7) and D(-2, 8)

  =  (0 - 2)/2, (7 + 8)/2

  =  -2/2, 15/2

  =  (-1, 15/2)

Hence ABCD is a parallelogram.

Question 2 :

A (−3, 2) , B (3, 2) and C (−3, −2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices.

Solution :

Mid point of BC  =  (3 + (-3))/2, (2 + (-2))/2

  = D (0, 0)

Distance between AD :

A(-3, 2) D(0, 0)

  =  √(x₂ - x₁)² + (y₂ - y₁)²

  =  √(-3-0)² + (2-0)²

  =  √9 + 4

  =  √13

C(-3, -2) D(0, 0)

  =  √(x₂ - x₁)² + (y₂ - y₁)²

  =  √(-3-0)² + (-2-0)²

  =  √9 + 4

  =  √13

B(3, 2) D(0, 0)

  =  √(x₂ - x₁)² + (y₂ - y₁)²

  =  √(0-3)² + (0-2)²

  =  √9 + 4

  =  √13

Hence the midpoint of the hypotenuse is equidistant from the vertices.

After having gone through the stuff given above, we hope that the students would have understood, "Practical Problems Using Midpoint Formula" 

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