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Find the Type of the Quadrilateral If Points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) Are Joined Serially. - Geometry

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Question

Find the type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially.

Solution

The given points are A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3).
If they are joined serially so, 
Slope of AB = \[\frac{- 7 + 2}{- 3 + 4} = - 5\]

Slope of BC = \[\frac{- 2 + 7}{3 + 3} = \frac{5}{6}\]

Slope of CD =\[\frac{3 + 2}{2 - 3} = - 5\]

Slope of AD = \[\frac{3 + 2}{2 + 4} = \frac{5}{6}\]

Opposite sides are parallel. 
AC = \[\sqrt{\left( 3 + 4 \right)^2 + \left( - 2 + 2 \right)^2} = \sqrt{49} = 7\]

BD = \[\sqrt{\left( 3 + 7 \right)^2 + \left( 2 + 3 \right)^2} = \sqrt{125} = 5\sqrt{5}\]

Diagonals are not equal.
Hence, the given points form a parallelogram.

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APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 5: Co-ordinate Geometry
Problem set 5 | Q: 18 | Page no. 123

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Solution Find the Type of the Quadrilateral If Points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) Are Joined Serially. Concept: Slope of a Line.
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