Co-ordinate Geometry

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Co-ordinate Geometry is the branch of mathematics in which a pair of two numbers, called co-ordinates, is used to represent the position of a point with respect to two mutually perpendicular number li

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In y = 3x + 5: - y is the dependent variable (its value depends on x) - x is the independent variable (we can choose any value for x) Since the equation is expressed with y as the subject, y depends o

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An ordered pair is a pair of two numbers written in a specific order, separated by a comma, and enclosed in small brackets. The order is important and necessary. Examples: (5, 7), (-3, 4), (0, -2) N

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When two ordered pairs are equal, their corresponding components are equal. (x + 2, 5) = (7, y - 1) First components: x + 2 = 7 ∴ x = 5 Second components: 5 = y - 1 ∴ y = 6 Therefore, x = 5 and y

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The four quadrants are: 1st Quadrant (XOY): Both x and y are positive (+, +) 2nd Quadrant (X'OY): x is negative, y is positive (-, +) 3rd Quadrant (X'OY'): Both x and y are negative (-, -) 4th Quadra

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Points on the x-axis: The y-coordinate is always 0, so coordinates are of the form (x, 0) Examples: (3, 0), (-5, 0), (0, 0) Points on the y-axis: The x-coordinate is always 0, so coordinates are of t

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Equation of x-axis: y = 0 (Because for every point on the x-axis, the y-coordinate is 0) Equation of y-axis: x = 0 (Because for every point on the y-axis, the x-coordinate is 0)

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x = 5 represents a vertical line parallel to the y-axis, passing through all points where x-coordinate is 5, such as (5, 0), (5, 2), (5, -4), etc. y = -3 represents a horizontal line parallel to the