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प्रश्न
Find the type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially.
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उत्तर
The given points are A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3).
If they are joined serially so,
\[\text{Slope of AB} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]
= \[\frac{-7 - (-2)}{-3 - (-4)}\]
= \[\frac{- 7 + 2}{- 3 + 4} = - 5\]
\[\text{Slope of BC} = \frac{y_2-y_1}{x_2-x_1}\]
= \[\frac{-2-(-7)}{3-(-3)}\]
= \[\frac{- 2 + 7}{3 + 3} = \frac{5}{6}\]
\[\text{Slope of CD} = \frac{y_2-y_1}{x_2-x_1}\]
= \[\frac{3-(-2)}{2-3}\]
= \[\frac{3 + 2}{2 - 3} = - 5\]
\[\text{Slope of AD} = \frac{y_2-y_1}{x_2-x_1}\]
= \[\frac{3-(-2)}{2-(-4)}\]
= \[\frac{3 + 2}{2 + 4} = \frac{5}{6}\]
Slope of AB = slope of CD
∴ line AB || line CD
Slope of BC = slope of AD
∴ line BC || line AD
Both the pairs of opposite sides of ∆ABCD are parallel.
∴ ABCD is a parallelogram.
∴ The quadrilateral formed by joining the points A, B, C and D is a parallelogram.
