Coordinate Geometry is a crucial branch of mathematics that blends algebra and geometry to study the positions of the points on a plane. It plays an essential role in the Class 9 syllabus forming the foundation for the more advanced topics in higher classes. Exercise 3.3 in Chapter 3 focuses on applying the principles of coordinate geometry to solve problems related to the distance between points the section formula and the area of a triangle.
Coordinate Geometry
Coordinate Geometry, introduced in Class 9, Chapter 3 is fundamental in understanding the relationship between algebraic equations and geometric shapes. Exercise 3.3 is an integral part of this chapter helping students solidify their understanding of plotting points calculating distances between points and determining geometric properties using coordinates. This exercise is vital as it lays the groundwork for more complex geometrical concepts that students will encounter in future classes.
Understanding Coordinate Geometry: Class 9 NCERT Solutions
Coordinate Geometry, a pivotal branch of mathematics, integrates algebra with geometry to analyze the position of points on a plane. In the Class 9 syllabus, Chapter 3 introduces fundamental concepts of Coordinate Geometry. Exercise 3.3, a key component of this chapter, focuses on essential topics such as plotting points, calculating distances between points, and determining geometric properties using coordinates. This exercise is crucial for building a solid foundation in coordinate geometry, which will be beneficial for more advanced mathematical studies.
Class 9 NCERT Mathematics Solutions - Exercise 3.3
Question 1: In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.
Solution:
(i) The point (-2, 4) lies in IInd Quadrant in the Cartesian plane as x coordinate is negative and the y coordinate is positive.
(ii) The point (3, -1) lies in IVth Quadrant in the Cartesian plane as x coordinate is positive and the y coordinate is negative.
(iii) The point (-1, 0) lies on the negative x-axis and the value of x coordinate is negative.
(iv) The point (1, 2) lies in Ist Quadrant in the Cartesian as both x and y are positive.
(v) The point (-3,-5) lies in the IIIrd Quadrant in the Cartesian plane as both x and y are negative.
Question 2: Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.
Solution:
We have to plot these points A(-2, 8), B(-1, 7), C(0, -1.25), D(1, 3) and E(3, -1).
Steps we have to use to plot these points,
- Let 1 unit represents 1 cm.
- To plot (-2, 8), we take (-2) units on x-axis and (+8) units on y-axis. Now we can plot A (-2, 8), it will lie in quadrant-II.
- To plot (-1, 7), we take (-1) units on x-axis and (+7) units on y-axis. Now we can plot B(-1, 7), it will lie in quadrant-II.
- To plot (0, -1.25), we will proceed (-1.25) units under the x-axis on the y-axis and mark the plot as C(0, -1.25), it will lie on the negative side of y-axis.
- To plot (1, 3), we take (+1) unit on x-axis and (+3) units on y-axis. Now we can plot D(1, 3), it will lie in quadrant-I.
- To plot (3, -1), we take (+3) units on x-axis and (-1) unit on y-axis. Now we can plot the point E(3, -1), it will lie in quadrant-IV.
