Welcome, students! In this lesson, we will explore step-by-step solutions for Class 9 Maths Chapter 3, Coordinate Geometry, Exercise 3.3. This exercise is designed to help you master the skills of identifying quadrants and plotting coordinates on a Cartesian plane according to the MP Board (NCERT) syllabus. Let's make learning math easy and enjoyable!
Exercise 3.3 Solutions
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:
To determine the quadrant or axis for each point, we look at the signs of the $x$-coordinate and $y$-coordinate:
- Quadrant I: $(+, +)$
- Quadrant II: $(-, +)$
- Quadrant III: $(-,-)$
- Quadrant IV: $(+, -)$
- On X-axis: $(x, 0)$
- On Y-axis: $(0, y)$
| Point | x-coordinate (Abscissa) | y-coordinate (Ordinate) | Location (Quadrant / Axis) |
|---|---|---|---|
| (-2, 4) | Negative (-) | Positive (+) | Quadrant II |
| (3, -1) | Positive (+) | Negative (-) | Quadrant IV |
| (-1, 0) | Negative (-) | Zero (0) | Negative X-axis |
| (1, 2) | Positive (+) | Positive (+) | Quadrant I |
| (-3, -5) | Negative (-) | Negative (-) | Quadrant III |
Verification: To verify, plot these points on a graph paper with standard X and Y axes intersecting at origin $O(0,0)$. You will observe that their positions perfectly match the analytical locations listed above.
Question 2
Plot the points $(x, y)$ given in the following table on the plane, choosing suitable units of distance on the axes:
| x | -2 | -1 | 0 | 1 | 3 |
|---|---|---|---|---|---|
| y | 8 | 7 | -1.25 | 3 | -1 |
Solution & Steps to Plot:
We write down the coordinate pairs from the table: $A(-2, 8)$, $B(-1, 7)$, $C(0, -1.25)$, $D(1, 3)$, and $E(3, -1)$.
- Draw horizontal line $X'OX$ (X-axis) and vertical line $Y'OY$ (Y-axis).
- Take scale: 1 unit = 1 cm on both axes.
- To plot A(-2, 8): Start from origin, move 2 units to the left on the negative x-axis, then move 8 units vertically upwards. Mark point $A$.
- To plot B(-1, 7): Move 1 unit left on the negative x-axis, then 7 units upwards. Mark point $B$.
- To plot C(0, -1.25): Since $x = 0$, the point lies on the y-axis. Move 1.25 units downwards on the negative y-axis (exactly one-quarter of the way between -1 and -2). Mark point $C$.
- To plot D(1, 3): Move 1 unit right on the positive x-axis, then 3 units upwards. Mark point $D$.
- To plot E(3, -1): Move 3 units right on the positive x-axis, then 1 unit downwards. Mark point $E$.
ЁЯЪА Aptitude Corner (For NTSE & Olympiads)
Topic: Reflections & Distance of Points
- Reflection across X-axis: The reflection of point $(x, y)$ across the X-axis is $(x, -y)$. (Only the sign of the y-coordinate changes).
- Reflection across Y-axis: The reflection of point $(x, y)$ across the Y-axis is $(-x, y)$. (Only the sign of the x-coordinate changes).
- Distance from Origin: The shortest straight-line distance of any point $P(x, y)$ from the origin $(0,0)$ is given by the formula:
Distance = $\sqrt{x^2 + y^2}$.
Example: The reflection of point $(-3, 5)$ across the Y-axis is $(3, 5)$. Its distance from the origin is $\sqrt{(-3)^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34}$ units.
With this, we have completed the final exercise of Coordinate Geometry! Practice plotting different points on a physical graph sheet to build strong spatial recognition skills. Keep studying, stay curious, and you'll ace your exams!
Academic Discussion & Doubts