The points A (–1, –2), B (4, 3), C (2, 5) and D (–3, 0) in that order form a rectangle. Is the following statement true or false

Solution:

Given, the points are A(-1, -2) B(4, 3) C(2, 5) and D(-3, 0)

We have to determine if the given points form a rectangle in the given order.

We know that the opposite sides of a rectangle are equal.

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

√[(x₂ - x₁)² + (y₂ - y₁)²]

The distance between A(-1, -2) and B(4, 3) = √[(4 - (-1))² + (3 - (-2))²]

= √[(5)² + (5)²]

= √(25 + 25)

= √50

AB = 5√2

The distance between B(4, 3) and C(2, 5) = √[(2 - 4)² + (5 - 3)²]

= √[(-2)² + (2)²]

= √(4 + 4)

= √8

BC = 2√2

The distance between C(2, 5) and D(-3, 0) = √[(-3 - 2)² + (0 - 5)²]

= √[(-5)² + (-5)²]

= √(25 + 25)

= √50

CD = 5√2

The distance between A(-1, -2) and D(-3, 0) = √[(-3 - (-1))² + (0 - (-2))²]

= √[(-2)² + (2)²]

= √(4 + 4)

= √8

AD = 2√2

It is clear that AB = CD and BC = AD

The opposite sides are equal.

Therefore, the given points form a rectangle.

✦ Try This: If AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0), then the length of its diagonal is

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

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NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 12

The points A (–1, –2), B (4, 3), C (2, 5) and D (–3, 0) in that order form a rectangle. Is the following statement true or false

Summary:

The statement “The points A (–1, –2), B (4, 3), C (2, 5) and D (–3, 0) in that order form a rectangle” is true as the opposite sides are equal

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