Ex 10.1, 9 - Without using distance formula, show that - Slope - Prependicularity

  1. Class 11
  2. Important Question for exams Class 11
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Ex10.1, 9 Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram. Let the given points be A (–2, –1) , B (4, 0) , C (3, 3) , D (–3, 2) We have to prove if ABCD is a parallelogram ABCD is a parallelogram if both pairs of opposite sides are parallel i.e. AB ∥ CD & AD ∥ BC So, we have to prove Slope of AB = Slope of CD Slope of AD = Slope of BC Lets calculate slope of AB, BC, CD, and AD Since Slope of AB = Slope of CD ∴ AB ∥ CD Since Slope of AD = Slope of BC ∴ AD ∥ BC Hence AB II CD & AD II BC Since both pairs of opposite sides of ABCD are parallel. Hence ABCD is a parallelogram

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