Class 10 Maths Chapter 7 Coordinate Geometry Important Questions

The beginning of the chapter introduces the Cartesian coordinate system, which is fundamental to coordinate geometry. It describes how this system uses two perpendicular lines, known as axes (the x-axis and the y-axis), to define a plane. Every point in this plane is represented by a pair of numerical coordinates: (x, y).

These coordinates indicate the point’s position relative to the two axes. The chapter 7 explains the concept of quadrants in the Cartesian plane and how the sign of the coordinates changes according to the quadrant in which a point lies. This understanding is crucial for locating points and navigating the coordinate plane.

We also learn here the concept of the distance formula is introduced. This formula is used to calculate the distance between any two points in the coordinate plane. The chapter 7 of 10th Maths derives the distance formula, from the Pythagorean theorem.

This formula becomes a fundamental tool in coordinate geometry for finding the lengths of line segments and is essential for solving various geometric problems, such as determining the perimeters and areas of shapes on the coordinate plane.

Class 10 Maths chapter 7 focus into the section formula, which is used to find the coordinates of a point that divides a line segment into a given ratio. The chapter 7 explains the two cases of the section formula: the internal division and the external division.

This concept is essential for problems involving partitioning line segments in a specific ratio, and it has applications in finding the centroids of triangles and other geometric figures in the coordinate plane.

Chapter 7 of 10th Maths also covers the concept of the area of a triangle formed by three given points in the coordinate plane. The formula for the area is derived and presented as an absolute value to ensure the area is always a positive quantity.

This part of the chapter 7 is important as it provides a method to calculate the area of a triangle when its vertices are known, using determinants. This method is a significant departure from traditional geometry and introduces students to an algebraic approach to solving geometric problems.

The class 10 Maths coordinate geometry discusses the concept of collinearity of points. The chapter 7 explains how the area of a triangle formula can be used to determine if three points are collinear.

If the area of a triangle formed by three points is zero, it implies that the points lie on a straight line, hence are collinear. This application of the area formula is crucial for understanding more complex geometric concepts and for solving problems involving the positioning of points in a plane.

The summary of the chapter summarizes the key concepts and highlights the importance of coordinate geometry in bridging algebraic and geometric concepts. It reinforces the skills of locating points in the Cartesian plane, calculating distances and midpoints, using the section formula, finding areas of triangles, and determining collinearity.

Important Questions of the chapter 7 concludes with a variety of problems and exercises designed to test the students’ understanding and application of these concepts. These exercises range from basic point plotting to more complex problems involving the calculation of areas and testing collinearity, ensuring a comprehensive grasp of coordinate geometry.