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Distance From Origin

The distance of a point from the origin in a Cartesian coordinate system is the length of the straight line segment connecting the point to the origin (0,0). It is calculated using a simplified version of the distance formula, which is directly derived from the Pythagoras Theorem.

Key Concepts

The origin is the reference point where the x-axis and y-axis intersect, always having the coordinates (0,0).

The distance is calculated by taking the square root of the sum of the squares of the point's x and y coordinates.

Since distance represents a physical length, the result of this calculation is always taken as a non-negative value, even if the coordinates are negative.

Formula & Equation

d = √(x^2 + y^2)

d is the distance from the origin, x is the x-coordinate (abscissa) of the point, and y is the y-coordinate (ordinate) of the point.

Common Misconceptions

Myth: Students often think that the distance from the origin can be negative if the point has negative coordinates, such as (-3, -4).

Fact: Distance is a scalar quantity representing length, so it is always positive. When you square negative coordinates, they become positive, ensuring the final square root yields a positive distance.

Real World Applications

A radar system at an airport acting as the origin to calculate the direct straight-line distance to an airplane located at specific coordinates in the sky.

A GPS tracking a delivery drone's direct displacement from its home base (0,0) to its current delivery drop-off point.

Frequently Asked Questions

What is the formula for the distance of a point from the origin?

The formula is d = √(x^2 + y^2), where x and y are the coordinates of the given point.

How is the distance from the origin related to the Pythagoras Theorem?

The x and y coordinates form the base and perpendicular of a right-angled triangle, with the distance from the origin acting as the hypotenuse.

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