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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 9 of 74
Marks: +1, -0
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.
Solution:  
Let A(–2, –1), B(4, 0), C(3, 3) and D(–3, 2) be the vertices of the given quadrilateral ABCD. Then,
Slope of AB = 0−(−1)4−(−2)\frac{0-(-1)}{4-(-2)} = 16\frac{1}{6}
Slope of DC = 3−23−(−3)\frac{3-2}{3-(-3)} = 16\frac{1}{6}
Slope of BC = 3−03−4\frac{3-0}{3-4} = 3−1\frac{3}{-1} = - 3
Slope of AD = 2−(−1)−3−(−2)\frac{2-(-1)}{-3-(-2)} = 3−1\frac{3}{-1} = - 3
Slope of AD = slope of BC ⇒ AD || BC
Slope of AB = Slope of CD ⇒ AB || CD
Hence, ABCD is a parallelogram.
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