VERTICES OF PARALLELOGRAM WORKSHEET

Vertices of parallelogram worksheet :

Here we are going to see some question to verify how to examine whether the given points are the vertices of parallelogram.

Vertices of parallelogram worksheet - Practice 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.

Vertices of parallelogram worksheet - Solution

Question 1 :

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

To show that the given points are collinear 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 (4,6), B (7,7), C (10,10) and D (7,9)

Distance between the points A and B

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 4, y₁ = 6, x₂ = 7  and  y₂ = 7

=  √(7-4)² + (7-6)²

=  √(3)² + (1)²

=  √9 + 1  =  √10

Distance between the points B and C

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 7, y₁ = 7, x₂ = 10  and  y₂ = 10

=  √(10-7)² + (10-7)²

=  √(3)² + (3)²

=  √9 + 9

=  √18 units

Distance between the points C and D

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 10, y₁ = 10, x₂ = 7  and  y₂ = 9

=  √(7-10)² + (9-10)²

=  √(-3)² + (-1)²

=  √9 + 1

=  √10 units

Distance between the points D and A

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 7, y₁ = 9, x₂ = 4  and  y₂ = 6

= √(4-7)² + (6-9)²

=  √(-3)² + (-3)²

=  √9 + 9

=  √18 units

AB = √10 units

BC = √18 units

CD = √10 units

DA = √18 units

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

Let us see the next problems on "Vertices of parallelogram worksheet"   "Vertices of parallelogram worksheet"

Question 2 :

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

Distance between the points A and B

√(x₂ - x₁)² + (y₂ - y₁)²

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

√(-5-3)² + (-4-(-5))²

=   √(-8)² + (-4+5)²

=  √64 + 1²

=  √(64 + 1)

=  √65 units

Distance between the points B and C

= √(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = -5, y₁ = -4, x₂ = 7  and  y₂ = 10

=  √(7-(-5))² + (10-(-4))²

=   √(7+5)² + (10+4)²

=   √12² + 14²

=   144 + 196

=  √340 units

Distance between the points C and D

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 7, y₁ = 10, x₂ = 15  and  y₂ = 9

=  √(15-7)² + (9-10)²

=   √(8)² + (-1)²

=   √64 + 1

=   √65 units

Distance between the points D and A

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 15, y₁ = 9, x₂ = 3  and  y₂ = -5

=  √(3-15)² + (-5-9)²

=  √(-12)² + (-14)²

=  √144 + 196

=  √340 units

AB = √65 units

BC = √340 units

CD = √65 units

DA = √340 units

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

Let us see the next problems on "Vertices of parallelogram worksheet"

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

Let us see the next problems on "Vertices of parallelogram worksheet"

Question 4 :

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

Distance between the points A and B

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 8, y₁ = 4, x₂ = 1  and  y₂ = 3

=  √(1-8)² + (3-4)²

=   √(-7)² + (-1)²

=  √49 + 1

=  √50 units

Distance between the points B and C

√(x₂ - x₁)² + (y₂ - y₁)²

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

=  √(3-1)² + (-1-3)²

=   √(2)² + (-4)²

=  √4 + 16

=  √20 units

Distance between the points C and D

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 3, y₁ = -1, x₂ = 4  and  y₂ = 6

=  √(4-3)² + (6-(-1))²

=  √(1)² + (6+1)²

=  √1 + 7²

=  √1 + 49

=  √50 units

Distance between the points D and A

√(x₂ - x₁)² + (y₂ - y₁)²

Here x₁ = 4, y₁ = 6, x₂ = 8  and  y₂ = 4

=  √(8-4)² + (4-6)²

=  √(4)² + (-2)²

=  √16 + 4

=  √20 units

AB = √50 units

BC = √20 units

CD = √50 units

DA = √20 units

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

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