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# Name the Quadrilateral Formed, If Any, by the Following Points, and Given Reasons for Your Answers: A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0) - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)

#### Solution

A (-1,-2) , B(1,0), C(-1,2), D(-3,0)

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((1 - (-1))^2 + (0 - (-2))^2)

=> AB=  sqrt((2)^2 + (2)^2)

=> AB = sqrt(4+ 4)

=> AB = 2sqrt2

Similarly

=> BC= sqrt((-1)-1)^2 + (2 - 0)^2

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

=> BC = sqrt(4 + 4)

=> BC= sqrt8

Similarly,

=> CD = sqrt((-3)-(-1)^2 + (0 - (2))^2)

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

=> CD = sqrt(4 + 4)

=> CD = sqrt8

=> CD = 2sqrt2

Also

=> DA = sqrt(((-1)-(-3))^2 + (0 -(-2))^2)

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

=> DA = sqrt(4 + 4)

=> DA = sqrt8

=> DA = 2sqrt2

Hence from above we see that all the sides of the quadrilateral are equal. Hence it is a square.

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Solution Name the Quadrilateral Formed, If Any, by the Following Points, and Given Reasons for Your Answers: A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0) Concept: Concepts of Coordinate Geometry.
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