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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.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, -4).
✓

Answer

False:
Any points (A) on perpendicular bisector will be equidistant from P and Q so,
PA = QA
or $PA^2 = QA^2$
$\Rightarrow (2 - 6)^2 + [7 - (5)]^2 = (2 - 0)^2 + [7 - (-4)]^2$
$\Rightarrow (-4)^2 + (2)^2 = 2^2 + (11)^2$
$\Rightarrow 16 + 4 = 4 + 121$
$\Rightarrow20\neq125$
So, A does not lie on the perpendicular bisector of PQ.

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