At Ramsetu, we aim to provide educational resources that make learning engaging and comprehensive. Chapter 7, “COORDINATE GEOMETRY,” from the 10th Class Mathematics textbook, covers the fundamental concepts of coordinate geometry, its properties, and applications. This chapter provides students with a thorough understanding of the Cartesian plane, plotting points, and solving geometrical problems using algebraic methods.
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Chapter Insights:
- Summary of “COORDINATE GEOMETRY.”
- Explanation of key concepts and properties.
- Detailed examples and exercises.
- Practical applications and relevance of coordinate geometry in everyday life.
Key Concepts and Definitions:
- Coordinate Geometry: The study of geometry using a coordinate system.
- Cartesian Plane: A plane defined by two perpendicular number lines: the x-axis and the y-axis.
- Coordinates: Ordered pairs that identify the position of points on the Cartesian plane.
- Distance Formula: A formula to find the distance between two points.
- Section Formula: A formula to find the coordinates of a point dividing a line segment in a given ratio.
- Midpoint Formula: A formula to find the midpoint of a line segment.
Chapter Content:
- Summary of “COORDINATE GEOMETRY”:
- Introduction to the Cartesian plane and coordinate system.
- Plotting points on the Cartesian plane.
- Understanding the concepts of the distance formula, section formula, and midpoint formula.
- Key Concepts:
- Coordinates: (x, y) where x is the abscissa and y is the ordinate.
- Distance Formula:
- Distance between two points (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) is given by (x2−x1)2+(y2−y1)2\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}(x2−x1)2+(y2−y1)2.
- Section Formula:
- The coordinates of a point dividing a line segment joining (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) in the ratio mare (mx2+nx1m+n,my2+ny1m+n)\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)(m+nmx2+nx1,m+nmy2+ny1).
- Midpoint Formula:
- The midpoint of a line segment joining (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) is (x1+x22,y1+y22)\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)(2×1+x2,2y1+y2).
- Formulas and Properties:
- Slope of a Line: m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}m=x2−x1y2−y1
- Equation of a Line:
- Slope-intercept form: y=mx+cy = mx + cy=mx+c
- Point-slope form: y−y1=m(x−x1)y – y_1 = m(x – x_1)y−y1=m(x−x1)
- Two-point form: y−y1=y2−y1x2−x1(x−x1)y – y_1 = \frac{y_2 – y_1}{x_2 – x_1}(x – x_1)y−y1=x2−x1y2−y1(x−x1)
- Applications:
- Real-life applications of coordinate geometry in navigation, architecture, engineering, and computer graphics.
- Using coordinate geometry to solve problems involving distances, midpoints, and areas of geometric shapes.