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The point A (2, 7) lies on the perpendicular bisector of line segment joining the points P (6, 5) and Q (0, – 4). Is the following statement true or false

Solution:

Given, the line segment joining the points P(6, 5) and Q(0, -4)

We have to determine if the point A(2, 7) lies on the perpendicular bisector of the 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 bisectors joining the two points are P(6, 5) and Q(0, -4)

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

i.e.,PA = QA

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

√[(x₂ - x₁)² + (y₂ - y₁)²]

The distance between the points P(6, 5) and A(2, 7) = √[(2 - 6)² + (7 - 5)²]

= √[(-4)² + (2)²]

= √(16 + 4)

= √20

= 2√5

The distance between the points Q(0, -4) and A(2, 7) = √[(2 - 0)² + (7 - (-4))²]

= √[(2)² + (11)²]

= √(4 + 121)

= √125

= 5√5

PA ≠ QA

Therefore, point A(2, 7) does not lie on the perpendicular bisector of the line segment joining the given points.

✦ Try This: Determine the point which lies on the perpendicular bisector of the line segment joining the points A(-2, -5) and B(2, 5) is

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

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 8

The point A (2, 7) lies on the perpendicular bisector of line segment joining the points P (6, 5) and Q (0, – 4). Is the following statement true or false

Summary:

The statement “The point A (2, 7) lies on the perpendicular bisector of the line segment joining the points P (6, 5) and Q (0, – 4)” is false as the distance between PA is not equal to QA

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