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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.
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(-1, 1) and B(3, 3).
✓

Answer

False:As the point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of the line joining the points A(-1, 1) and B(-3, 3), then point P must be equidistant from A and B. So, we must write PA = PB.
$\Big[\because\text{ d}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}\Big]$
$\text{PA}=\sqrt{(-1-0)^2+(1-2)^2}$
$\text{PA}=\sqrt{1+1}=\sqrt{2}\text{ units}$
$\text{PB}=\sqrt{(3-0)^2+(3-2)^2}$
$\text{PB}=\sqrt{9+1}=\sqrt{10}\text{ units}$
$\therefore\text{PA}\neq\text{PB}$
Hence the given statement is false.

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