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Home » 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).
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).
CBSE | Class 10 | Coordinate Geometry | Exercise 7.2 | Maths | NCERT Exemplar
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).

Solution:

The statement given in the question is false.

Justification:

We know that the points on the perpendicular bisector of the line segment joining two points are equidistant from the two points, i.e., PA should be equals to the PB.

Now using distance formula,

d~=\text{ }\surd \text{ }({{({{x}_{2}}~\text{ }{{x}_{1}})}^{2}}~+\text{ }{{({{y}_{2}}~\text{ }{{y}_{1}})}^{2}})

PA=\sqrt{{{\left[ -4-\left( 4 \right) \right]}^{2}}+{{\left( 6-2 \right)}^{2}}}

PA=\sqrt{{{\left( 0 \right)}^{2}}+{{\left( 4 \right)}^{2}}}=4

PB=\sqrt{{{\left[ -4-4 \right]}^{2}}+{{\left( -6-2 \right)}^{2}}}

PB=\sqrt{{{0}^{2}}+{{\left( -8 \right)}^{2}}}=8

As a result, PA is not equal to PB.

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