## VERTICES OF PARALLELOGRAM QUESTION3

Vertices of parallelogram question3 :

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 question3 - Solution

Question 3 :

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

Distance between the points A and B

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = -4, y₁ = -3, x₂ = 3  and  y₂ = 1

=  √(3-(-4))² + (1-(-3))²

=   √(3+4)² + (1+3)²

=  √7² + 4²

=  √49 + 16

=  √65 units

Distance between the points B and C

√(x₂ - x₁)² + (y₂ - y₁)²

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

=  √(3-3)² + (6-1)²

=   √(0)² + (5)²

=   √0 + 25

=  √25 units

Distance between the points C and D

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 3, y₁ = 6, x₂ = -4  and  y₂ = 2

√(-4-3)² + (2-6)²

=   √(-7)² + (-4)²

=  √49 + 16

=  √65 units

Distance between the points D and A

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = -4, y₁ = 2, x₂ = -4  and  y₂ = -3

=  √(-4-(-4))² + (-3-2)²

=   √(-4+4)² + (-5)²

=  0 + 25

=  √25 units

AB = √65 units

BC = √25 units

CD = √65 units

DA = √25 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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