Coordinate Geometry geometry using a coordinate system.

What is Coordinate Geometry?

• Coordinate Geometry is the study of geometry using a coordinate system.

• It helps us locate points, lines, and shapes on a plane using numbers instead of just shapes.

2. The Coordinate Plane

• Made up of two perpendicular lines:

  1. X-axis → horizontal line

  2. Y-axis → vertical line

• The point where these axes meet is called the origin.

• The plane is divided into four quadrants:

  1. Quadrant I → both x and y positive

  2. Quadrant II → x negative, y positive

  3. Quadrant III → both x and y negative

  4. Quadrant IV → x positive, y negative

3. Coordinates of a Point

• Every point on the plane is represented by an ordered pair: (x, y)

  • x = distance along the X-axis

  • y = distance along the Y-axis

• Example (conceptual): (3, 4) → move 3 units along X-axis, then 4 units along Y-axis

4. Distance Between Two Points

• The distance is how far apart two points are on the plane.

• It can be found using visual methods like counting squares or understanding horizontal and vertical separation.

5. Midpoint of a Line Segment

• The midpoint is the point exactly in the middle of a line joining two points.

• Conceptually, it is like averaging the positions of the two points.

6. Slope of a Line (Conceptual)

• Slope shows how steep a line is.

• Positive slope → line rises from left to right

• Negative slope → line falls from left to right

• Zero slope → horizontal line

• Undefined slope → vertical line

7. Key Points for Exams

• Coordinate plane = X-axis + Y-axis; origin = intersection.

• Quadrants: I, II, III, IV; know the signs of x and y.

• Point = (x, y) → x = horizontal, y = vertical.

• Distance = how far points are.

• Midpoint = center of line segment.

• Slope = steepness of a line (positive, negative, zero, undefined).