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Point P (0, 2) is the point of intersection of the y–axis and perpendicular bisector of the line segment joining the points A (–1, 1) and B (3, 3). Is the following statement true or false

Solution:

Given, a line segment joining the points A(-1, 1) and B(3, 3)

We have to determine if the point P(0, 2) is the point of intersection of the y-axis and perpendicular bisector of the given line segment.

We know that any point lying on the perpendicular bisector of the line segment joining two points is equidistant from the two points.

The perpendicular bisector joining the two points are A(-1, 1) and B(3, 3)

To check if the point P lies on the perpendicular bisector, then distance between PA must be equal to distance between PB

i.e.,PA = PB

The distance between two points P (x₁ , y₁) and Q (x₂ , y₂) is

√[(x₂ - x₁)²+(y₂ - y₁)²]

To find distance between P(0, 2) and A(-1, 1)

PA = √[(-1 - 0)²+(1 - 2)²] = √[(-1)²+(-1)²] = √(1+1) = √2

To find distance between P(0, 2) and B(3, 3)

PB = √[(3 - 0)²+(3 - 2)²] = √[(3)²+(1)²] = √(9+1) = √10

It is clear that PA ≠ PB

Therefore, point P(0, 2) does not lie on the perpendicular bisector of the line segment.

✦ Try This: Check if the point P (0, 4) is the point of intersection of the y–axis and perpendicular bisector of the line segment joining the points A (1, -2) and B (3, 4).

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 4

Point P (0, 2) is the point of intersection of the y–axis and perpendicular bisector of the line segment joining the points A (–1, 1) and B (3, 3). Is the following statement true or false

Summary:

The statement “Point P (0, 2) is the point of intersection of the y–axis and perpendicular bisector of the line segment joining the points A (–1, 1) and B (3, 3)” is false as it fails to satisfy the condition that the point lying on the perpendicular bisector of the line segment is equidistant from the two points.

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