**Vertices of parallelogram question7 :**

Here we are going to see practice question on 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.

**Question 7 :**

Examine whether the given points A (0,3) and B (4,4) and C (6,2) and D (2,1) 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 (0,3) and B (4,4) and C (6,2) and D (2,1)

Distance between the points A and B

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 0, y₁ = 3, x₂ = 4 and y₂ = 4**

**= ** √(4-0)² + (4-3)²

= √(4)² + (1)²

= ** **√16 + 1

= √17 units

Distance between the points B and C

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 4, y₁ = 4, x₂ = 6 and y₂ = 2**

**= ** √(6-4)² + (2-4)²

= √(2)² + (-2)²

= ** **√4 + 4

= √8 units

Distance between the points C and D

= **√(x₂ - x₁)² + (y₂ - y₁)²**

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

**= ** √(2-6)² + (1-2)²

= √(-4)² + (-1)²

= ** **√16 + 1

= √17 units

Distance between the points D and A

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 2, y₁ = 1, x₂ = 0 and y₂ = 3**

**= ** √(0-2)² + (3-1)²

= √(-2)² + (2)²

= ** **√4 + 4

= √8 units

AB = √17 units

BC = √8 units

CD = √17 units

DA = √8 units

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

(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.

- Solution for vertices of parallelogram question 1
- Solution for vertices of parallelogram question 2
- Solution for vertices of parallelogram question 3
- Solution for vertices of parallelogram question 4
- Solution for vertices of parallelogram question 5
- Solution for vertices of parallelogram question 6
- Solution for vertices of parallelogram question 7

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