Coordinate Geometry

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The x-coordinate or abscissa of a point is the distance of that point from the y-axis. It represents the horizontal position of the point on the coordinate plane.

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The y-coordinate or ordinate of a point is the distance of that point from the x-axis. It represents the vertical position of the point on the coordinate plane.

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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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The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by: PQ = √[(x₂ - x₁)² + (y₂ - y₁)²]. This formula is derived using the Pythagoras theorem.

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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 distance formula: AB = √[(6-3)² + (8-4)²] = √[3² + 4²] = √[9 + 16] = √25 = 5 units. Therefore, the distance between A(3, 4) and B(6, 8) is 5 units.

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When both points lie on the x-axis, the distance is simply |b - a| or |a - b|. This is because the y-coordinates are both 0, so the distance formula simplifies to the absolute difference of x-coordina…