VERTICES OF PARALLELOGRAM QUESTION5

Vertices of parallelogram question5 :

Here we are going to see practice question on vertices of parallelogram.

How to test whether the given points are vertices of parallelogram ?

(i)  Find the length of all sides using distance between two points formula

(ii)  In a parallelogram the midpoints of the diagonal will be equal.

(iii)  If the given vertices satisfies one of the above conditions, then we can say the given points form a parallelogram.

Vertices of parallelogram question5 - Solution

Question 5 :

Examine whether the given points  A (5,8) and B (6,3) and C (3,1) and D (2,6) forms a parallelogram.

Solution :

To show that the given points forms a rectangle we need to find the distance between three points.

Distance Between Two Points (x ₁, y₁) and (x₂ , y₂)

√(x₂ - x₁)² + (y₂ - y₁)²


Four points are A (5,8) and B (6,3) and C (3,1) and D (2,6)

Distance between the points A and B

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 5, y₁ = 8, x₂ = 6  and  y₂ = 3

=    √(6-5)² + (3-8)²

=    √(1)² + (-5)²

=    √1 + 25

=    √26 units

Distance between the points B and C

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 6, y₁ = 3, x₂ = 3  and  y₂ = 1

=    √(3-6)² + (1-3)²

=    √(-3)² + (-2)²

=    √9 + 4

=    √13 units

Distance between the points C and D

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 3, y₁ = 1, x₂ = 2  and  y₂ = 6

=    √(2-3)² + (6-1)²

=    √(-1)² + (5)²

=    √1 + 25

=    √26 units

Distance between the points D and A

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 2, y₁ = 6, x₂ = 5  and  y₂ = 8

=    √(5-2)² + (8-6)²

=    √(3)² + (2)²

=    √9 + 4

=    √13 units

AB = √26 units

BC = √13 units

CD = √26 units

DA = √13 units

Length of opposite sides are equal. So the given vertices forms a parallelogram.

Try other questions

(1)  Examine whether the given points  A (4,6) and B (7,7) and C (10,10) and D (7,9) forms a parallelogram.

(2)  Examine whether the given points  A (3,-5) and B (-5,-4) and C (7,10) and D (15,9) forms a parallelogram.

(3)  Examine whether the given points  A (-4,-3) and B (3,1) and C (3,6) and D (-4,2) forms a parallelogram.

(4)  Examine whether the given points  A (8,4) and B (1,3) and C (3,-1) and D (4,6) forms a parallelogram.

(5)  Examine whether the given points  A (5,8) and B (6,3) and C (3,1) and D (2,6) forms a parallelogram.

(6)  Examine whether the given points  A (6,1) and B (5,6) and C (-4,3) and D (-3,-2) forms a parallelogram.

(7)  Examine whether the given points  A (0,3) and B (4,4) and C (6,2) and D (2,1) forms a parallelogram.

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