NCERT Class 10 Maths Chapter 7 - Coordinate Geometry"

Introduction:

NCERT Class 10 Maths Chapter 7, "Coordinate Geometry," introduces students to the fascinating world of coordinates and the Cartesian plane. This chapter lays the groundwork for understanding the relationship between algebra and geometry by exploring how points, lines, and shapes can be represented using numerical coordinates. In this blog, we'll provide a detailed overview of the solutions provided by NCERT for the exercises in Chapter 7, offering concise explanations to help students grasp the concepts more effectively.

Understanding Coordinate Geometry:

Coordinate geometry is like a GPS for mathematics; it helps us locate points, draw lines, and solve geometric problems using numerical coordinates.

The Cartesian Plane:

• The Cartesian plane is a two-dimensional plane formed by two perpendicular number lines called the x-axis and y-axis.

• Each point in the plane is uniquely identified by a pair of coordinates (x, y), where x represents the horizontal distance from the y-axis (called the abscissa) and y represents the vertical distance from the x-axis (called the ordinate).

Basic Concepts:

1. Distance Formula:

   • The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is calculated using the distance formula: √((x₂ - x₁)² + (y₂ - y₁)²).

   • This formula is derived from the Pythagorean theorem and represents the length of the hypotenuse of a right triangle formed by the two points.

2. Section Formula:

   • The coordinates of a point dividing a line segment joining two points with coordinates (x₁, y₁) and (x₂, y₂) in a given ratio m:n are given by: ((mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n)).

   • This formula helps in finding the coordinates of a point located at a specific ratio along a line segment.

Detailed Solutions:

Let's delve into the detailed solutions for the exercises provided in NCERT Class 10 Maths Chapter 7:

1. Exercise 7.1:

   • This exercise focuses on plotting points on the Cartesian plane and finding the distance between them.

   • Solutions include identifying the coordinates of points, plotting them on the plane, and applying the distance formula to calculate distances.

2. Exercise 7.2:

   • In this exercise, students encounter problems involving finding the coordinates of points dividing line segments in a given ratio.

   • Solutions include applying the section formula to find the coordinates of the desired points based on the given ratios.

3. Exercise 7.3:

   • This exercise deals with finding the area of triangles formed by joining points on the Cartesian plane.

   • Solutions involve applying the shoelace formula or the formula for the area of a triangle given its vertices' coordinates.

Conclusion:

NCERT Class 10 Maths Chapter 7 - Coordinate Geometry serves as a gateway to understanding the intricate relationship between algebraic expressions and geometric shapes. By mastering the detailed solutions provided in this chapter, students gain a deeper appreciation for the power of coordinates in solving geometric problems. As students navigate through the exercises, they develop essential problem-solving skills and build a strong foundation in coordinate geometry, setting the stage for more advanced mathematical concepts in the future.

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