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Home » Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
CBSE | Class 10 | Coordinate Geometry | Maths | NCERT
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

(i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)

(ii) (- 3, 5), (3, 1), (0, 3), (- 1, – 4)

Solution:

(i) Let the points (- 1, – 2), (1, 0), ( – 1, 2), and ( – 3, 0) represent the quadrilateral’s vertices A, B, C, and D, respectively.

AB=\sqrt{{{\left( 1+1 \right)}^{2}}+{{\left( 0+2 \right)}^{2}}}=\sqrt{4+4}=2\sqrt{2}

BC=\sqrt{{{\left( -1-1 \right)}^{2}}+{{\left( 2-0 \right)}^{2}}}=\sqrt{4+4}=2\sqrt{2}

CD=\sqrt{{{\left( -3+1 \right)}^{2}}+{{\left( 0-2 \right)}^{2}}}=\sqrt{4+4}=2\sqrt{2}

DA=\sqrt{{{\left( -3+1 \right)}^{2}}+{{\left( 0-2 \right)}^{2}}}=\sqrt{4+4}=2\sqrt{2}

AC=\sqrt{{{\left( -1+1 \right)}^{2}}+{{\left( 2+2 \right)}^{2}}}=\sqrt{0+16}=4

BD=\sqrt{{{\left( -3-1 \right)}^{2}}+{{\left( 0-0 \right)}^{2}}}=\sqrt{16+0}=4

Length of side= AB = BC = CD = DA = 2\sqrt 2

Measure of diagonal = AC = BD = 4

As a result, the specified points are the vertices of square.

(ii) The vertices A, B, C, and D of the given quadrilateral are represented by the points (- 3, 5), (3, 1), (0, 3), and ( – 1, – 4).

AB=\sqrt{{{\left( -3-3 \right)}^{2}}+{{\left( 1-5 \right)}^{2}}}=\sqrt{36+16}=2\sqrt{13}

BC=\sqrt{{{\left( 0-3 \right)}^{2}}+{{\left( -4-3 \right)}^{2}}}=\sqrt{9+4}=\sqrt{13}

CD=\sqrt{{{\left( -1-0 \right)}^{2}}+{{\left( -4-3 \right)}^{2}}}=\sqrt{1+49}=5\sqrt{2}

AD=\sqrt{{{\left( -1+3 \right)}^{2}}+{{\left( -4-5 \right)}^{2}}}=\sqrt{4+81}=\sqrt{85}

Points A, B, and C are also seen to be collinear.
As a result, the given points can only form a triangle with three sides, rather than a quadrilateral with four sides.
As a result, the given points cannot form a quadrilateral in general.

i

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