Question

Write the coordinates of point p on x axis which is equidistant from the points a(-2,0) and b(6,0).​

Answer 1

Answer:

The coordinates of point P are (2,0).

Step-by-step explanation:

The given points are A(-2,0) and B(6,0).​ Both points are lie on x-axis because the y-coordinate is 0.

We have to find the point P on x axis which is equidistant from the points.

Since both point lie on x-axis, therefore P is the midpoint of A and B.

Therefore the coordinates of point P are (2,0).

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Answer 2

Answer:

Step-by-step explanation:

Given :-

Points are (-2, 0) and (6, 0)

To Find :-

Coordinates of point P

Solution :-

Let the coordinates of P on the x-axis(x, 0)

Taking A(-2, 0) and B(6, 0)

Here,    PA = PB

$\implies\sqrt{(x \: + \: 2)^2 \: + \: (0 \: - \: 0)^2} \: \: = \: \sqrt{(x \: +6)^2 \: + \: (0 \: - \: 0)^2}$

$\implies \: \sqrt{(x \: + \: 2)^2} \: = \: \sqrt{(x \: - \: 6)^2}$

On Squaring Both sides, we get

⇒ (x + 2)² = (x - 6)²

⇒ x² + 4 + 4x = x² + 36 - 12x

⇒ 4 + 4x = 36 - 12x

⇒ 16x = 32

⇒ $x=\frac{32}{16}$

⇒ x = 2

Hence, the coordinates of P are (2, 0).