Find the coordinates of the point on y-axis which is nearest to the point (–2, 5).

We have

Given is the point A(-2, 5).

Let B(0, a) be the point to be found on y-axis, where its x coordinate will be 0.

So, distance from A to B, i.e., AB needs to be the shortest.

Let’s find AB.

We know the formula for distance in coordinate geometry.

Let x₁ = -2, x₂ = 0, y₁ = 5 and y₂ = a.

AB is given by,

Substituting the values, we get

⇒

Now, for AB to be minimum or shortest (a – 5)² must equal to 0.

⇒ (a – 5)² = 0

⇒ a – 5 = 0

⇒ a = 5

Thus, we have got the point B(0, a) = B(0, 5)

So, coordinate of the point on y-axis nearest to point (-2, 5) is (0, 5).