Search intent refers to the task behind a user’s online query and is one of the three core elements of SEO practices. This is especially important when trying to find the point nearest the origin on a plane. It is essential to identify the intent of your users to ensure that audiences find the information, product, or page for the purpose they are actively seeking.

## Understand the Problem

Finding the point nearest the origin on a plane is a geometrical task that requires basic knowledge of geometry and algebra. The origin is the point (0, 0) in a two-dimensional plane where the two axes meet, and the task entails finding the point having the least or minimum distance from this origin among all the given points.

In mathematical terms, the task involves finding the point (x _{i }, y _{i }) having the minimum distance $$ d=\sqrt{(0-x_i)^2 + (0-y_i)^2}$$ among all the points (x _{1 }, y _{1 }), (x _{2 }, y _{2 })… (x _{n }, y _{n }).

##Solution through Algebraic Manipulation

The distance of any point (x _{i } , y _{i }) from the origin is given by the expression:

$$ d=\sqrt{(0-x_i)^2 + (0-y_i)^2}$$

Where x _{i } and y _{i } are the coordinates of the point.

The expression can be simplified to $$ d^2 = (x_i)^2 + (y_i)^2 $$

So, we need to find the point which has the least value for the expression $$ d^2=(x_i)^2 + (y_i)^2$$

It is given that the coordinates of the points have values and we have to compare different points to find the point which has the least value for the expression $$ d^2=(x_i)^2 + (y_i)^2$$

Hence, we can find the point nearest to the origin by comparing the values of $$(x_i)^2 + (y_i)^2 $$ among all the points (x_{1}, y_{1}),(x_{2}, y_{2})...(x_{n}, y_{n}). The point (x_{i}, y_{i}) which has the least value for the expression $$(x_i)^2 + (y_i)^2 $$ is the point which is nearest to the origin.

## Sources & Further Reading

## Frequently Asked Questions (FAQ)

### What is Search Intent?

Search intent is the task behind a user's online query also known as user intent. It is one of the three core elements of SEO practices and refers to understanding a user's search query so that the most relevant results can be found.

### What is the origin point?

In a two-dimensional plane, the origin is the point (0, 0) where the two axes meet.

### How do I determine the point nearest the origin on a plane?

To determine the point nearest the origin on a plane, you need to identify the point (xi, yi) with the least distance from the origin point which can be obtained by comparing the values of the expression $$(x_i)^2 + (y_i)^2 $$ among all the points.

### What do I need to know to find the point nearest the origin on a plane?

You would need a basic knowledge of algebra and geometry to understand the task of finding the point nearest the origin on a plane.

### Are there any resources I can use for finding the point nearest the origin on a plane?

Yes, you can find resources available online to help you with the task of finding the point nearest the origin on a plane. Some of the resources include GeeksforGeeks and MathOpenRef.