Coordinate Geometry

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The x-coordinate or abscissa of a point is the distance of the point from the y-axis. It tells us how far left or right the point is from the vertical axis.

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The y-coordinate or ordinate of a point is the distance of the point from the x-axis. It tells us how far up or down the point is from the horizontal axis.

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The coordinates of a point lying on the x-axis are of the form (x, 0), where x can be any real number and the y-coordinate is always 0.

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The coordinates of a point lying on the y-axis are of the form (0, y), where y can be any real number and the x-coordinate is always 0.

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Distance Formula: The distance between two points P(x₁, y₁) and Q(x₂, y₂) is PQ = √[(x₂ - x₁)² + (y₂ - y₁)²]. Use this formula to find the distance between any two points in a coordinate plane.

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Using distance formula: AB = √[(6-3)² + (8-4)²] = √[3² + 4²] = √[9 + 16] = √25 = 5 units

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The distance of point P(x, y) from the origin O(0, 0) is OP = √(x² + y²). This is a special case of the distance formula where one point is the origin.

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Using the formula for distance from origin: OP = √(5² + 12²) = √(25 + 144) = √169 = 13 units