7. COORDINATE GEOMETRY

7. COORDINATE GEOMETRY

  • 7

    Coordinate Geometry

    This section introduces coordinate geometry, focusing on the distance formula and how to find points that divide line segments.

  • 7.1

    Introduction

    In this section, coordinate geometry is introduced, focusing on locating points in a plane using coordinate axes, and the basics of plotting and understanding distances between points.

  • 7.2

    Distance Formula

    The Distance Formula helps to calculate the distance between two points in a coordinate plane using their coordinates.

  • 7.3

    Section Formula

    The Section Formula provides a method to determine the coordinates of a point that divides a line segment into a specified ratio.

  • 7.4

    Summary

    This section summarizes the main concepts in coordinate geometry including the distance formula and section formula.

    • Key Summary

    This chapter explores the fundamentals of coordinate geometry, focusing primarily on the distance between points and the section formula for dividing line segments. It emphasizes the relationship between algebra and geometry through various examples and concepts, such as forming triangles and determining collinearity among points. The introduction of key formulas and the exploration of real-life applications exemplify the significance of coordinate geometry in numerous fields.

    Key Takeaways

    • The distance formula for two points P(x1, y1) and Q(x2, y2) is given by PQ = √[(x2 - x1)² + (y2 - y1)²].
    • The coordinates of a point P, which divides a line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n are derived using the section formula.
    • The mid-point of a line segment can be calculated using the average of the coordinates of the endpoints.

    Key Concepts

    • Distance Formula: A mathematical equation used to determine the distance between two points in a coordinate plane.
    • Section Formula: A formula used to find the coordinates of a point that divides a line segment into a specific ratio.