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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
Question
State whether the following statements are true or false. Justify your answer.
Points A(4, 3), B(6, 4), C(5, -6) and D(-3, 5) are the vertices of a parallelogram.
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Answer

False:The diagonals of parallelogram bisect each othere so, ABCD will be a parallelogram if,
mid-point of diagonal AC = mid-point of diagonal BD
$\Rightarrow\Big(\frac{\text{x}_1+\text{x}_2}{2},\frac{\text{y}_1+\text{y}_2}{2}\Big)=\Big(\frac{\text{x}'_1+\text{x}'_2}{2},\frac{\text{y}'_1+\text{y}'_2}{2}\Big)$
$\Rightarrow\Big(\frac{4+5}{2},\frac{-6+3}{3}\Big)=\Big(\frac{6-3}{4+5}\Big)$
$\Rightarrow\Big(\frac{9}{2},\frac{-3}{2}\Big)\neq\Big(\frac{3}{2},\frac{9}{2}\Big)$
Hence ABCD is not a parallelogram.

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