Grade 9 Co-ordinate Geometry

Coordinate Plane: A two-dimensional plane formed by two perpendicular number lines, usually called the x-axis and the y-axis.

X-axis: The horizontal number line.

Y-axis: The vertical number line.

Origin: The point where the x-axis and y-axis intersect. Its coordinates are (0, 0).

Quadrants: The two axes divide the plane into four regions called quadrants. They are numbered I, II, III, and IV, starting from the top right and going counter-clockwise.

Coordinates: Every point on the coordinate plane can be uniquely identified by an ordered pair of numbers (x, y).

X-coordinate (Abscissa): The first number in the ordered pair. It represents the horizontal distance of the point from the y-axis. A positive x-coordinate means the point is to the right of the y-axis; a negative x-coordinate means it's to the left.

Y-coordinate (Ordinate): The second number in the ordered pair. It represents the vertical distance of the point from the x-axis. A positive y-coordinate means the point is above the x-axis; a negative y-coordinate means it's below.

Notation: The coordinates are written as (x, y) with the x-coordinate first, followed by the y-coordinate, enclosed in parentheses.
Example: The point (3, 2) is located 3 units to the right of the y-axis and 2 units above the x-axis.

Step 1: Start at the Origin (0, 0).

Step 2: Move horizontally along the x-axis according to the x-coordinate. Move right for positive x, left for negative x.
Example: To plot point (3, 2), move 3 units to the right from the origin.

Step 3: From the position reached in Step 2, move vertically parallel to the y-axis according to the y-coordinate. Move up for positive y, down for negative y.
From 3 units right, move 2 units up.

Step 4: Mark the point at this final position. This is the location of the point with the given coordinates.
Mark the point at the position reached after moving 3 units right and 2 units up from the origin.

Result: The point (3, 2) is plotted on the coordinate plane.

Distance from Y-axis: The distance of a point (x, y) from the y-axis is the absolute value of its x-coordinate, which is |x|.
Example: The distance of point (3, 2) from the y-axis is |3| = 3 units.

Distance from X-axis: The distance of a point (x, y) from the x-axis is the absolute value of its y-coordinate, which is |y|.
Example: The distance of point (3, 2) from the x-axis is |2| = 2 units.

Note: Distance is always a non-negative value, which is why we use the absolute value.