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Points A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) are the vertices of a parallelogram. Is the following statement true or false

Solution:

Given, the points are A(4, 3) B(6, 4) C(5, -6) and D(-3, 5)

We have to determine if the given points are the vertices of a parallelogram.

By the property of parallelogram,

The opposite sides of a parallelogram are equal.

The distance between two points P (x₁ , y₁) and Q (x₂ , y₂) is

√[(x₂ - x₁)²+(y₂ - y₁)²]

AB = √[(6 - 4)²+(4 - 3)²]

= √[(2)²+(1)²]

= √(4 + 1)

AB = √5

BC = √[(5 - 6)²+(-6 - 4)²]

= √[(-1)²+(-10)²]

= √(1 + 100)

BC = √101

CD = √[(-3 - 5)²+(5 - (-6))²]

= √[(-8)²+(11)²]

= √(64 + 121)

CD = √185

AD = √[(-3 - 4)²+(5 - 3)²]

= √[(-7)²+(2)²]

= √(49 + 4)

AD = √53

It is clear that AB ≠ CD and BC ≠ AD

The opposite sides are not equal.

Therefore, the given points are not the vertices of a parallelogram.

✦ Try This: The fourth vertex D of a parallelogram ABCD whose three vertices are A(- 2, 3), B(6, 7) and C(8, 3) is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 6

Summary:

The statement “Points A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) are the vertices of a parallelogram” is false as the opposite sides are not equal

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