Coordinates are P (x,y) and O (0,0)..

By Distance Formula,,,

PQ = √x^2 + √y^2..

Distance of a Point from the Origin

To find the distance between a point P(x, y) and the origin (0, 0) in a two-dimensional Cartesian coordinate system, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and calculates the distance between two points in a plane. In this case, we are finding the distance between the origin and point P.

The Distance Formula:
The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Where:
- (x1, y1) represents the coordinates of the first point (in this case, the origin),
- (x2, y2) represents the coordinates of the second point (in this case, point P),
- d represents the distance between the two points.

Applying the Distance Formula to Find the Distance from the Origin:
In this case, we are finding the distance from the origin to point P(x, y).

1. Substitute the values into the distance formula:
- (x1, y1) = (0, 0) (coordinates of the origin)
- (x2, y2) = (x, y) (coordinates of point P)

d = √((x - 0)^2 + (y - 0)^2)
= √(x^2 + y^2)

2. Simplify the expression:
- Since we are interested in only the magnitude of the distance, we can remove the square root and work with the squared expression.

d^2 = x^2 + y^2

3. Finally, take the square root of the squared expression to obtain the distance:
- The distance, d, is the positive square root of the sum of the squares of the coordinates.

d = √(x^2 + y^2)

Conclusion:
The distance of a point P(x, y) from the origin can be found by using the distance formula. By substituting the coordinates of the origin and the point into the formula, simplifying the expression, and taking the square root of the squared expression, we can determine the distance.