Maths · Distance formula, sections formula, locus and its equation
The points \) , C(4,0), D(2,3) \) are the vertices of
The points \( \boldsymbol{A}(-4,1) \) \( B(-2,-2), C(4,0), D(2,3) \) are the vertices of
- A. parallelogram
- B. rectangle
- C. rhombus
- D. None of these
Step-by-step solution
Compute vectors: AB = (2, -3), BC = (6, 2), CD = (-2, 3), DA = (-6, -2). AB = -CD and BC = -DA, so opposite sides are parallel and equal, hence a parallelogram. Adjacent sides are not perpendicular (AB·BC = 6 ≠ 0), so not a rectangle. Sides are not all equal (|AB| = √13, |BC| = √40), so not a rhombus.
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