Coordinate Geometry Ex 3.3 Class 9 NCERT Solutions & Concepts

Welcome back, future mathematicians! Today on YoLearn AI, we are diving deep into the concepts of coordinate geometry ex 3 3 class 9 ncert. In previous exercises, we learned about the Cartesian plane, the axes, and writing the coordinates of a point. Now, we will master the application: how to plot coordinates onto a two-dimensional graph sheet and identify their respective quadrants or axes. Exercise 3.3 is a highly scoring part of the CBSE Class 9 maths curriculum because it translates basic logic into visual practice. In this guide, we provide step-by-step processes, common mistakes to watch out for, and interactive-style practice questions to build your graphing confidence. Whether you are using our YoLearn sketchpad or study sheets, this guide will make plotting points simple and intuitive!

Plotting Points on the Cartesian Plane: Rules & Conventions

In class 9 maths coordinate geometry ex 3 3, the central skill is plotting. Let us review the coordinate pair (x, y). The first number, x, is the abscissa (distance along the horizontal x-axis). The second number, y, is the ordinate (distance along the vertical y-axis). Together, they define a unique position on the plane. To accurately place these points, you must understand the signs of coordinates inside each quadrant:

  • Quadrant I (+, +): Both x and y are positive (e.g., (3, 5)).
  • Quadrant II (-, +): x is negative, y is positive (e.g., (-2, 4)).
  • Quadrant III (-, -): Both x and y are negative (e.g., (-3, -5)).
  • Quadrant IV (+, -): x is positive, y is negative (e.g., (1, -3)).

If either coordinate is 0, the point lies directly on one of the axes. For instance, any point with the form (x, 0) lies on the x-axis, and any point of the form (0, y) lies on the y-axis. The origin (0, 0) is where both axes intersect.

Step-by-Step Process to Plot a Point (x, y)

  1. Start at the Origin — Always place your pencil tip at the origin (0, 0), where the horizontal x-axis and vertical y-axis meet.
  2. Move Horizontally for x-coordinate — If x is positive, move 'x' units to the right along the x-axis. If x is negative, move 'x' units to the left. If x is 0, stay at the origin.
  3. Move Vertically for y-coordinate — From that current horizontal position, move 'y' units upwards if y is positive, or move 'y' units downwards if y is negative. If y is 0, do not move up or down.
  4. Mark and Label the Point — Mark the final location with a small dot, circle it, and write the coordinates next to it, such as P(x, y).

Common Graphing Mistakes & Board Exam Tips

Avoid these typical errors to secure maximum marks in your class assessments:

  1. Swapping x and y Coordinates: This is the most common mistake. Remember that (2, -3) is completely different from (-3, 2). The horizontal value (abscissa) must always be selected first.
  2. Confusing Axis Locations with Quadrants: Points like (5, 0) or (0, -3) do not belong to any quadrant. They lie strictly on the x-axis and y-axis, respectively.
  3. Scale Selection: If your coordinates contain fractional decimals (like -1.25), choose a scale where 1 unit equals 2 cm (or 10 small divisions) so that you can accurately plot decimal values on your graph sheet.
  4. Labeling Your Graph: Always draw and label axes as XOX' and YOY'. Write down the chosen scale in the top right corner of your sheet.

Practice Questions with Solutions

  • Q: In which quadrant or on which axis do the points (-2, 4), (3, -1), (-1, 0), and (1, 2) lie? A: Step 1: Analyze (-2, 4). The x-coordinate is negative and the y-coordinate is positive. This corresponds to Quadrant II. Step 2: Analyze (3, -1). The x-coordinate is positive and the y-coordinate is negative. This corresponds to Quadrant IV. Step 3: Analyze (-1, 0). The y-coordinate is zero, which means the point lies on the x-axis (specifically, the negative x-axis). Step 4: Analyze (1, 2). Both x and y coordinates are positive. This corresponds to Quadrant I. Final answer: (-2, 4) is in Quadrant II; (3, -1) is in Quadrant IV; (-1, 0) is on the x-axis; (1, 2) is in Quadrant I.
  • Q: Plot the point (0, -3.5) on the Cartesian plane and state its location. A: Step 1: Identify the coordinates: x = 0 and y = -3.5. Step 2: Start at the origin (0, 0). Since x is 0, there is no horizontal movement. Step 3: Since y is -3.5, move 3.5 units downwards along the negative y-axis. Step 4: Mark this point between -3 and -4 on the y-axis. Final answer: The point (0, -3.5) lies on the negative y-axis.
  • Q: Find the coordinates of a point which lies on the negative side of the x-axis at a distance of 4 units from the origin. A: Step 1: The point lies on the x-axis, which means its ordinate (y-coordinate) must be 0. Step 2: It lies on the negative side of the x-axis, meaning its x-coordinate is negative. Step 3: The distance from the origin is 4 units, so the abscissa (x-coordinate) is -4. Final answer: The coordinates of the point are (-4, 0).
  • Q: Plot the points A(1, 1), B(2, 2), and C(3, 3) on a Cartesian plane. Are these points collinear? A: Step 1: Plot A(1, 1) by moving 1 unit right and 1 unit up. Step 2: Plot B(2, 2) by moving 2 units right and 2 units up. Step 3: Plot C(3, 3) by moving 3 units right and 3 units up. Step 4: Place a ruler along points A, B, and C. You will see they all lie on the same straight diagonal line. Final answer: Yes, the points A, B, and C are collinear as they lie on the straight line described by the equation y = x.

Frequently Asked Questions

How do we know if a point lies on an axis?

A point lies on an axis if at least one of its coordinates is zero. If the x-coordinate is zero, the point lies on the y-axis, and if the y-coordinate is zero, it lies on the x-axis.

Why is the origin written as (0, 0)?

The origin is the starting point of reference where both horizontal and vertical distances are zero. Therefore, both its abscissa and ordinate are 0.

What does 'collinear points' mean in coordinate geometry?

Collinear points are three or more points that lie on the exact same straight line when plotted on a Cartesian plane.