Question

Find the distance of point $P(x, y)$ from the origin.

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Answer

To find the distance of a point $P(x, y)$ from the origin, we start by understanding the coordinates of the origin, which are $(0, 0)$.

The formula for the distance between any two points $(x_1, y_1)$ and $(x_2, y_2)$ in a Cartesian plane is given by the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

In this case, the second point is the origin $(0,0)$ and the first point is $P(x,y)$. Plugging in these values, we thus have:

$$ d = \sqrt{(0 - x)^2 + (0 - y)^2} $$

This simplifies to:

$$ d = \sqrt{x^2 + y^2} $$

Therefore, the distance of the point $P(x, y)$ from the origin is:

$$ \sqrt{x^2 + y^2} $$

This represents the Euclidean distance from the origin to the point $P$ in the plane.


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