Question

Point P(x, y) is equidistant from points A(7, 1) and B(3, 5).

Statement (1): \[x=\frac{7+3}{2}\] and \[y=\frac{1+5}{2}\]. 

Statement (2): \[(x-7)^{2}+(y-1)^{2}=(x-3)^{2}+(y-5)^{2}\]

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

It is given that point P(x, y) is equidistant from points A(7, 1) and B(3, 5).

If a point is equidistant from two points it is not necessary that it will be the mid-point of the two points, sp we cannot use mid-point formula to find the co-ordinates of P.

So, statement 1 is false.

Using distance formula,

Distance between two points = `sqrt((x_2 - x_1)^2 + (y_2 - y_1))`

⇒ PA = PB

⇒ `sqrt((x − 7)^2 + (y − 1)^2) = sqrt((x − 3)^2 + (y − 5)^2)`

⇒ (x − 7)² + (y − 1)² = (x − 3)² + (y − 5)²

So, statement 2 is true.