Question

Find the coordinates of the point on x-axis which is nearest to the point (2, -4).

Answer 1

Given that the point lies on x-axis, so the y-coordinate will be 0.

Let the given point be A(2,-4).

Let the required coordinate be B(p,0).

Now,

x1 = 2, y1 = -4, x2 = p. y2 = 0.

$= > AB = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

$= > \sqrt{(p - 2)^2 + (0 + 4)^2}$

Now,

The minimum of the expression p - 2 is 0.

= > p - 2 = 0

= > p = 2.

Therefore, the required coordinate is (2,0).

Hope this helps!