## VERTICES OF PARALLELOGRAM QUESTION6

Vertices of parallelogram question6 :

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 question6 - Solution

Question 6 :

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

Distance between the points A and B

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 6, y₁ = 1, x₂ = 5  and  y₂ = 6

=    √(5-6)² + (6-1)²

=    √(-1)² + (5)²

=    √1 + 25

=    √26 units

Distance between the points B and C

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 5, y₁ = 6, x₂ = -4  and  y₂ = 3

=    √(-4-5)² + (3-6)²

=    √(-9)² + (-3)²

=    √81 + 9

=    √90 units

Distance between the points C and D

√(x₂ - x₁)² + (y₂ - y₁)²

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

=    √(-3-(-4))² + (-2-3)²

=    √(-3+4)² + (-5)²

=    √1² + 25

=    √26 units

Distance between the points D and A

√(x₂ - x₁)² + (y₂ - y₁)²

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

=    √(6-(-3))² + (1-(-2))²

=    √(6+3)² + (1+2)²

=    √9² + 3²

=    √81 + 9

=    √90 units

AB = √26 units

BC = √90 units

CD = √26 units

DA = √90 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.

## Related topics

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