Question

Find the relation between x and y if point P (x, y) lies on the perpendicular bisector of the line joining the points (7, 1) and (3, 5).

Answer 1

Answer:

P(x, y) = P(5,3).

Step-by-step explanation:

As per the question,

Let us consider the line AB, where A = (7,1) and B  (3,5).

MN is the perpendicular bisector of line AB, that means line MN bisects the line AB in two equal parts.

Point P(x, y) lies on the perpendicular bisector of the line MN which bisects the line AB.

Therefore, point P is the mid point of line AB.

Ans the co-ordinates of point P is given by:

x = (x₁+x₂)/2  

x=(7+3)/2

=5

y = (y₁+y₂)/2

y = ( 1+5)/2

=3

P(x, y) = P(x, y)

Hence the co-ordinate o relation of P(x, y) = P(5,3).

Answer 2

Answer:

P(x, y) = P(5,3)

Step-by-step explanation:

As per the question,

Let us consider the line AB, where A = (7,1) and B  (3,5).

MN is the perpendicular bisector of line AB, that means line MN bisects the line AB in two equal parts.

Point P(x, y) lies on the perpendicular bisector of the line MN which bisects the line AB.

Therefore, point P is the mid point of line AB.

Ans the co-ordinates of point P is given by:

x = (x₁+x₂)/2  

x=(7+3)/2

=5

y = (y₁+y₂)/2

y = ( 1+5)/2

=3

P(x, y) = P(x, y)

Hence the co-ordinate o relation of P(x, y) = P(5,3).