In the ICSE Class 9 Mathematics curriculum, Coordinate Geometry is a fundamental topic that introduces students to the concept of coordinates and graphs. Here’s a summary of the key points covered in this topic:
1. **Cartesian Coordinate System**: Introduces the Cartesian coordinate system, consisting of two perpendicular lines (x-axis and y-axis) intersecting at the origin (0,0).
2. **Coordinates of a Point**: Explains how to locate a point in the plane using its coordinates (x, y), where x is the horizontal distance from the y-axis (abscissa) and y is the vertical distance from the x-axis (ordinate).
3. **Distance Formula**: Introduces the distance formula √[(x₂ – x₁)² + (y₂ – y₁)²], which is used to find the distance between two points in a plane.
4. **Section Formula**: Discusses the section formula, which is used to find the coordinates of a point that divides a line segment into two parts in a given ratio.
5. **Midpoint Formula**: Introduces the midpoint formula [(x₁ + x₂)/2, (y₁ + y₂)/2], which is used to find the coordinates of the midpoint of a line segment.
6. **Gradient of a Line**: Defines the gradient (slope) of a line and explains how to find it using the formula (y₂ – y₁)/(x₂ – x₁) for two points (x₁, y₁) and (x₂, y₂) on the line.
7. **Equation of a Line**: Discusses how to find the equation of a line given its gradient and a point on the line, using the point-slope form y – y₁ = m(x – x₁), where m is the gradient and (x₁, y₁) is the given point.
8. **Parallel and Perpendicular Lines**: Explains the concepts of parallel and perpendicular lines in terms of their gradients.
9. **Graphs of Linear Equations**: Shows how to graph linear equations in two variables (y = mx + c) by plotting points and drawing the line.
10. **Intercepts**: Defines the x-intercept and y-intercept of a line and explains how to find them from the equation of the line.
Coordinate Geometry is a foundational topic that helps students understand the relationship between algebraic equations and geometric shapes, laying the groundwork for more advanced topics in mathematics.