Question

12. The point A (2, 7) lies on the perpendicular bisector of line segment joining the points P (6,5) and
Q (0,4).​ check whether true or false

Answer 1

Answer:

Step-by-step explanation

The point A(2,7) bisect p(6,5) and Q(0,4)

So, A is the mid-point of line PQ then co-ordinates of A must be(x₁+x₂/2, y₁+y₂/2)

⇒ x₁+x₂/2= 6+0/2= 6/2= 3

and

⇒y₁+y₂/2=5+4/2= 9/2= 4.5

From this co-ordinates of A is (3,4.5)

But it is given that co-ordinates of A is (2,7)

hence,this statement is false

Answer 2

Answer:

Step-by-step explanation:

Answer :-

False

If A (2, 7) lies on the perpendicular bisector of P (6, 5) and Q(0, - 4),

Therefore,

AP = AQ

Then,

By using Distance formula,

⇒ AP = √(6 - 2)² + (5 - 7)²

⇒ AP = √(4)² + (- 2)²

⇒ AP = √20

And,

⇒ AQ = √(0 - 2)² + (- 4 - 7)²

⇒ AQ = √(- 2)² + (- 11)²

⇒ AQ = √125

As, AP ≠ AP

Therefore,

A does not lie on the perpendicular bisector of PQ.