Coordinate Geometry Class 9 Important Questions Free PDF Download

Coordinate Geometry is one of the most fundamental chapters in Class 9 Mathematics, and its concepts are crucial not only for understanding geometry but also for solving problems related to distances, midpoints, and plotting points on a graph. As you prepare for your exams, it's essential to focus on the key topics from this chapter that often appear in both objective and subjective questions. Whether you're trying to master the distance formula, understand the coordinates of points, or learn how to find the midpoint between two points, this chapter offers a strong foundation for advanced math topics in higher classes.

In this blog, we will discuss the most important questions from Chapter 3: Coordinate Geometry, which will help you sharpen your understanding and improve your problem-solving skills. These questions cover all the essential concepts, from basic plotting to applying formulas for distance and midpoint, ensuring you’re well-prepared to tackle any exam challenge with confidence.

Let’s dive in and explore some of the most frequently asked questions that will help you ace your exam and build a solid understanding of Coordinate Geometry!

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Chapter 3 Coordinate Geometry Important Questions

1. In the forest, rain shelters are at an interval of 2 km along paved roads. A forest ranger is travelling on Road x. He crosses a rain shelter located at (3, 0). What is likely to be the location of the next shelter? 

Solutions:

Given that the rain shelters are spaced 2 km apart along paved roads and the ranger crosses a rain shelter at location (3, 0), we can infer the following:

• The rain shelters are likely placed at intervals of 2 km along the road, either in the positive or negative direction along the x or y-axis.
• The position of the shelter at (3, 0) suggests that the shelters could be placed on a coordinate grid where each shelter is 2 km away from the previous one along the x-axis.

If the ranger is traveling on the road and the next shelter is at a 2 km interval, we can look at the next possible positions by adding or subtracting 2 km along the x-axis or y-axis. Therefore, the next shelter could be at one of the following likely positions:

• (5, 0) — 2 km ahead along the x-axis.
• (1, 0) — 2 km back along the x-axis.
• (3, 2) — 2 km ahead along the y-axis.
• (3, -2) — 2 km back along the y-axis.

The most likely location for the next shelter, assuming the ranger is traveling along the x-axis, would be (5, 0).

2. The control room receives a message about trespassers located at (–9, –8). The trespassers were seen moving towards Road x on foot. The ranger immediately dispatches a team of guards in a jeep towards them. The guards encounter the trespassers before crossing Road x. Which of the following is most likely to be the location of the encounter? 

a. (–9, –14)

b. (–9, –5)

c.(–9, 4)

d. (9, 5)

Solutions:

‍(b) (–9, –5)

Explanations:

Given that the trespassers are located at (−9,−8) and are moving towards Road x on foot, we know that Road x is likely a line along the x-axis, i.e., the line where the y-coordinate is 0. The guards are travelling towards them in a jeep, and they encounter the trespassers before crossing Road xxx, meaning the encounter happens when the trespassers are still moving towards the x-axis.

To determine the likely location of the encounter, we consider that the trespassers are moving towards the x-axis. Their initial position is (−9,−8), so their movement is likely along the vertical direction (y-axis), towards increasing y-values. This means they are moving from (−9,−8) towards a point where the y-coordinate is closer to 0, but not yet reaching 0.

Thus, the most probable location for the encounter is where the trespassers are still moving up but haven't crossed the x-axis yet. Among the given options, the point (−9,−5) is the most likely, as it represents a point closer to the x-axis (y = -5) without crossing it.

3. Ravi planted a red maple tree sapling. The height of the sapling is 0.25 m. The average growth rate of the height of a red maple tree is 0.27 m per year. The average life of a red maple tree is 80–100 years. Ravi estimated that his tree would grow up to 27 m. What is the likely reason behind his estimation? 

Solutions:

Ravi's estimation that the red maple tree would grow up to 27 m is likely based on a misunderstanding of the growth rate or the expected size of the tree. Let's analyze the situation:

• The height of the sapling is 0.25 m.
• The average growth rate is 0.27 m per year.
• The tree’s average life is 80–100 years.

If the tree grows at a rate of 0.27 m per year for, say, 100 years (the maximum life expectancy), the total growth would be:

Total growth=0.27 m/year×100 years

= 27m

This aligns with Ravi's estimation, but there is a flaw in this reasoning:

• A tree’s growth is not always linear throughout its life. The growth rate can vary with age, and trees tend to grow faster in their early years and slow down as they mature.
• The final height of the tree is likely to be much smaller than the total growth potential calculated by Ravi, considering that growth rates typically decrease with age.

Therefore, the likely reason behind Ravi's estimation is that he may have assumed that the tree would maintain a constant growth rate (0.27 m per year) throughout its entire life, without accounting for the natural slowdown in growth as the tree ages. This would be an overestimation of the final height of the tree.

4. Which of the following is true for the line with equation: 1.x+0.y-4=0?

a. The distance of the line from the x-axis is 1

b. The distance of the line from the Y-axis is 4. 

c. The distance of the line from the Y-axis is –1. 

d. The distance of the line from the x-axis changes from 1 to –4. 

Solutions:

(b) The distance of the line from the Y-axis is 4. 

Explanations:

Let's analyze the equation of the line:

1x+0y−4=0

which simplifies to:

x=4

This is a vertical line that intersects the x-axis at x=4. It is parallel to the y-axis, meaning it has a constant distance from the y-axis.

Now, let's go through the options:

1. The distance of the line from the x-axis is 1: This is false. The line is vertical and does not change its distance from the x-axis as it moves along the y-axis. Its distance from the x-axis is not 1.
2. The distance of the line from the Y-axis is 4: This is true. Since the line is vertical and located at x=4, the distance from the line to the y-axis (which is the vertical distance to the line x=0) is exactly 4 units.
3. The distance of the line from the Y-axis is –1: This is false. The distance cannot be negative because distance is always a non-negative quantity.
4. The distance of the line from the x-axis changes from 1 to –4: This is false. The distance from the x-axis is fixed and does not change as the line is vertical. The line doesn't cross the x-axis, so there's no change in the distance.

5. Which of the following equations represents the height (h) of the red maple tree after ‘t’ years of planting?

a. h=0.25+0.27 

b. h=0.25t+0.27

c. h=0.25+0.27t

d. h=0.25-0.27t

Solutions:

(c) h=0.25+0.27t

Explanations: 

To represent the height h of the red maple tree after t years, let's break down the given information:

• The initial height of the sapling is 0.25 m (at t=0).
• The tree grows at an average rate of 0.27 m per year.

The general formula for the height of the tree after t years is:

h=initial height+(growth rate×t)

Substituting the given values:

h=0.25+0.27t

Thus, the correct equation for the height of the tree after t years is:

h=0.25+0.27t

Chapter 3 Coordinate Geometry Important Concepts

Coordinate geometry is all about studying geometry using a coordinate system. The system is based on a Cartesian plane, which is a two-dimensional system that helps us find the position of points. The plane has two axes: the x-axis (horizontal) and the y-axis (vertical). The point where these axes intersect is called the origin, represented as (0, 0).

Key Concepts:

Coordinates of a Point:

Every point on the plane is represented by an ordered pair (x, y). Here, x is the horizontal distance from the origin (left or right), and y is the vertical distance (up or down).

For example, (3, 4) means the point is 3 units to the right of the origin and 4 units above it.

Plotting Points:

To plot a point, you start at the origin. Move along the x-axis based on the x-coordinate, then move along the y-axis based on the y-coordinate. The point where these two movements meet is the plotted point.

Quadrants:

The coordinate plane is divided into 4 parts called quadrants:

Quadrant I: Both x and y are positive.

Quadrant II: x is negative, y is positive.

Quadrant III: Both x and y are negative.

Quadrant IV: x is positive, y is negative.

Distance Formula:

To find the distance between two points (x₁, y₁) and (x₂, y₂), we use the distance formula:

d=√(x2​−x1​)²+(y2​−y1​)²

This formula helps calculate the straight-line distance between two points on the plane.

Midpoint Formula:

The midpoint is the point exactly halfway between two points. For points (x₁, y₁) and (x₂, y₂), the midpoint M is given by:

M= ((x1​+x2)/2, (y1​+y2)/2)

This formula gives the average of the x-coordinates and the y-coordinates of the two points.

This chapter teaches you how to work with points and find relationships between them using a simple number system. It's helpful for solving real-world problems involving distances and positions, like in maps or computer graphics.

Chapter 3 Coordinate Geometry Important Questions: Why

Chapter 3 of Class 9 Mathematics, Coordinate Geometry, is vital because it serves as a bridge between algebra and geometry. It allows students to understand geometric shapes, distances, and positions through algebraic equations and formulas. This chapter is not only foundational for the current class but also for future classes in mathematics, particularly in the study of higher-level geometry and calculus.

Here’s why focusing on important questions from this chapter is essential for your exam preparation:

Conceptual Clarity: The important questions often highlight the core concepts of the chapter, like plotting points, using the distance formula, and finding the midpoint. By practicing these questions, you reinforce your understanding and gain better clarity on how the concepts apply in real-world scenarios.

High Frequency in Exams: Many exams, including the CBSE board exams, feature questions based on the distance and midpoint formula, or the plotting of points on a coordinate plane. These concepts are frequently tested in both objective and subjective forms. By solving key questions, you get a better understanding of what to expect in the exam.

Problem-Solving Skills: Solving important questions improves your ability to apply the formulas in different contexts, which is a crucial part of mathematics. Whether it's calculating the distance between two points or finding the midpoint of a segment, regular practice will help you solve problems quickly and accurately.

Building a Strong Foundation: Coordinate Geometry is not just limited to Class 9. It forms the foundation for studying 2D and 3D geometry in future classes. Mastering this chapter will make advanced topics like straight lines, circles, and conic sections much easier in later years.

Boost Confidence: Solving important questions repeatedly helps build your confidence. The more problems you solve, the better prepared you’ll be, and this will help reduce exam anxiety. You will feel more comfortable tackling unfamiliar problems when you’ve already encountered similar ones in your practice.

Score Better Marks: Since the questions in this chapter are easy to understand but require precision, solving important questions will ensure that you are not only able to solve them correctly but also quickly. This will help you maximize your marks in the shortest amount of time during the exam.

In summary, focusing on the important questions of Coordinate Geometry will not only help you understand the core concepts but also ensure that you are fully prepared for your exam. It strengthens your foundation in mathematics, builds confidence, and improves your problem-solving speed, which are all key to achieving success in your exams! 

Chapter 3 Coordinate Geometry Important Questions: How

Understanding the "how" of solving important questions in Coordinate Geometry is just as crucial as understanding the concepts themselves. This chapter involves practical application of formulas and the ability to interpret graphical information. Here’s a step-by-step guide on how to approach the important questions in this chapter:

Understand the Basics First

Before diving into questions, make sure you have a solid understanding of the coordinate system, the coordinates of points, and how to plot them. Review the concepts of the x-axis, y-axis, and the origin. This foundational knowledge will help you understand the context of most questions.

Steps:

• Review how to plot points and locate them on the Cartesian plane.
• Recall the difference between the four quadrants and how to interpret coordinates in each quadrant.

Understand Important Formulas

A big part of this chapter involves using formulas for distance and midpoint calculations. Make sure you have these formulas memorized and understand their application.

d=√(x2​−x1​)²+(y2​−y1​)²

M= ((x1​+x2)/2, (y1​+y2)/2)

Practice applying these formulas to various problems to get comfortable with them.

Read the Question Carefully

Whether the question asks for the distance between two points or the midpoint, make sure to understand what is being asked. Identify the coordinates given in the problem and determine what needs to be calculated.

Steps to Follow:

• Carefully note the coordinates of the points involved in the problem.
• Look for clues in the question that suggest whether you need to find the distance, midpoint, or other related information.

Apply the Appropriate Formula

Once you've identified the correct formula to use (distance or midpoint), plug in the values from the question.

For Distance Problems:

• Use the distance formula and substitute the x and y values of the two points.
• Simplify the expression step by step.

For Midpoint Problems:

• Use the midpoint formula to calculate the average of the x-coordinates and y-coordinates.

Double-Check Your Calculations

After solving, it's essential to double-check your work, especially when calculating square roots or averages. Ensure you've substituted the correct values into the formulas and that your final answer makes sense in the context of the problem.

Quick Check:

• For distance problems, verify that the result is a positive number (since distance cannot be negative).
• For midpoint problems, check that the result represents a point that lies between the two given points.

Practice Variety Questions

To gain proficiency, solve a variety of problems from your textbook, previous years’ exams, and sample papers. This helps you understand different ways in which the formulas and concepts can be applied.

Example Questions to Practice:

• Find the distance between two points.
• Determine the midpoint of a segment.
• The plot given points and identify their coordinates.
• Identify the coordinates of a point in a given quadrant.
• Solve word problems related to coordinates (e.g., finding the distance between two towns on a map).

Understand the Application of the Concept

Coordinate Geometry isn’t just about using formulas; it’s about understanding how these concepts apply to real-world situations. For example, the distance formula can be used in map reading, architecture, and navigation.

We hope that you practise the above important questions of ‘Coordinate Geometry’ and achieve your dream marks.

All the Best