What type of a quadrilateral do the points A (2, –2), B (7, 3), C (11, –1) and D (6, –6) taken in that order, form

Solution:

Given, the points are A(2, -2) B(7, 3) C(11, -1) and D(6, -6)

We have to find the type of a quadrilateral formed by the given points.

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

√[(x₂ - x₁)² + (y₂ - y₁)²]

Distance between A(2, -2) and B(7, 3) = √[(7 - 2)² + (3 - (-2))²]

= √[(5)² + (5)²]

= √(25 + 25)

= 5√2

Distance between B(7, 3) and C(11, -1) = √[(11 - 7)² + (-1 - 3)²]

= √[(4)² + (-4)²]

= √(16 + 16)

= 4√2

Distance between C(11, -1) and D(6, -6) = √[(6 - 11)² + (-6 - (-1))²]

= √[(-5)² + (-5)²]

= √(25 + 25)

= 5√2

Distance between A(2, -2) and D(6, -6) = √[(6 - 2)² + (-6 - (-2))²]

= √[(4)² + (-4)²]

= √(16 + 16)

= 4√2

Distance between A(2, -2) and C(11, -1) = √[(11 - 2)² + (-1 - (-2))²]

= √[(9)² + (1)²]

= √(81 + 1)

= √82

Distance between B(7, 3) and D(6, -6) = √[(6 - 7)² + (-6 - 3)²]

= √[(-1)² + (-9)²]

= √(81 + 1)

= √82

We observe that AB = CD and BC = AD.

Also, AC = BD

The opposite sides of the quadrilateral are equal.

The diagonals of the quadrilateral are equal.

Therefore, the given points represent a rectangle.

✦ Try This: Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:(-1, -2), (1, 0), (-1, 2), (-3, 0)

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

NCERT Exemplar Class 10 Maths Exercise 7.3 Problem 3

What type of a quadrilateral do the points A (2, –2), B (7, 3), C (11, –1) and D (6, –6) taken in that order, form

Summary:

The type of a quadrilateral formed by the points A (2, –2), B (7, 3), C (11, –1) and D (6, –6) taken in that order is a rectangle as the opposite sides and diagonals are equal

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