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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

ConceptSlope of a Line

#### 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.

Is there an error in this question or solution?

#### 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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