Question

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

Answer 1

Answer :

Coordintes of required point - (0, 5).

Step-by-step explanation:

Given :

Point on y-axis (-2,5).

To Find :

The coordinates.

Solution :

A - (-2, 5)

So,

The required point is in y-axis, It's x - coordinate should be zero (0).

★ Consider the -

Firstly we have to find coordinates of the point 'B' and distance AB is small.

So,

Finding the point AB :

$\sf\\\implies x_1=-2,\;y_1 = 5.\\ \\\implies x_2 = 0,\;y_2 = a$

$\bigstar\;\textbf{\underline{\underline{The value of AB - }}}\\\sf\\\implies AB = \sqrt{(x_2-x_1)^2 + (y_1 -y_2)^2}\\ \\\implies \sqrt{(0-(-2))^2 +(a-5)^2}\\ \\\implies \sqrt{(2)^2 - (a-5)^2}\\ \\\implies \sqrt{(6)^2 +(a-5)^2}\\ \\\implies AB = a-5 = 0\\ \\\implies So,a = 5.$

∴ Coordintes of required point - (0, 5).

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Formulae used -

★ (a + b)² = a² + 2ab + b²

★ ( a - b)² = a² - 2b + b²            { Extra formula }