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# Name the Quadrilateral Formed, If Any, by the Following Points, and Given Reasons for Your Answers: A(4, 5) B(7, 6), C (4, 3), D(1, 2) - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

A(4, 5) B(7, 6), C (4, 3), D(1, 2)

#### Solution

A (4, 5), B (7,6), C(4,3), D(1,2)

Let A, B, C and D be the four vertices of the quadrilateral ABCD.

We know the distance between two points P(x_1,y_1) and Q(x_2, y_2)is given by distance formula:

PQ = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)

Hence

=> AB = sqrt((7 - 4)^2 + (6 - 5)^2)

=> AB = sqrt((-3)^2 + (-3)^2)

=> AB = sqrt(9 + 1)

=> AB = sqrt(10)

Similarly,

=> BC = sqrt((4 - 7)^2 + (3 - 6)^2)

=> BC = sqrt((-3)^2 + (1)^2)

=> BC= sqrt(9  + 9)

=> BC = sqrt18

Similarly

=> CD = sqrt((1 - 4)^2 + (2 - 3)^2)

=> CD = sqrt((-3)^2 + (-1)^2)

=> CD = sqrt(9 + 1)

=> CD = sqrt(9 + 1)

=> CD = sqrt10

Also

=> DA = sqrt((1 - 4)^2 + (2 -5)^2)

=> DA = sqrt((-3)^2 + (-3)^2)

=> DA = sqrt(9 + 9)

=> DA = sqrt18`

Hence from above we see that

AB = CD and BC = DA

Hence from above we see that

AB = CD and BC = DA

Here opposite sides of the quadrilateral is equal. Hence it is a parallelogram

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Solution Name the Quadrilateral Formed, If Any, by the Following Points, and Given Reasons for Your Answers: A(4, 5) B(7, 6), C (4, 3), D(1, 2) Concept: Concepts of Coordinate Geometry.
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