Distance from Axes: CBSE Class 10 Sample Paper 2025-26 Std Q2

Coordinate geometry can seem abstract when you’re just learning formulas, but Question 2 from the CBSE Class 10 Standard Sample Paper 2025 brings us back to basics with a beautifully simple yet conceptual problem. This 1-mark question tests whether you truly understand what coordinates mean and how distance from axes works in the Cartesian plane.

Today, we’re going to explore a question that many students rush through, missing the deeper concept it teaches. The question asks: “What is the shortest distance (in units) of the point (2, 3) from the y-axis?”

Simple enough, right? But this question is a perfect example of why understanding concepts is more important than memorizing formulas. Let’s dive in!

The Question

The shortest distance (in units) of the point (2, 3) from the y-axis is:

• a) 2
• b) 3
• c) 5
• d) 1

Understanding the Coordinate System

Before we solve, let’s refresh what coordinates mean.

When we say a point is at (2, 3), we’re saying:

• Move 2 units along the x-axis (horizontal direction) from the origin
• Then move 3 units parallel to the y-axis (vertical direction)
• The point where you land is (2, 3)

The x-coordinate tells us how far the point is from the y-axis. The y-coordinate tells us how far the point is from the x-axis.

This is the key insight that makes this question trivial once you understand it!

Step-by-Step Solution

Step 1: Visualize the Problem

Let’s draw the coordinate axes:

• Draw the x-axis (horizontal line)
• Draw the y-axis (vertical line perpendicular to x-axis)
• Mark the origin O where they intersect

Step 2: Plot the Point (2, 3)

Starting from origin:

• Move 2 units to the right along the x-axis → reach point (2, 0)
• From (2, 0), move 3 units up parallel to y-axis → reach point (2, 3)

Now you have your point plotted in the first quadrant!

Step 3: Understand “Shortest Distance”

Here’s the crucial concept: The shortest distance between a point and a line is always the perpendicular distance.

Think of it like this: if you want to reach a wall from where you’re standing, the shortest path is to walk straight toward it (perpendicular), not at an angle!

Step 4: Drop a Perpendicular to Y-Axis

We need to find the shortest distance from point (2, 3) to the y-axis.

Drop a perpendicular from (2, 3) to the y-axis. Where does it land? At point (0, 3)!

Notice something interesting? The perpendicular to the y-axis is parallel to the x-axis. This is because:

• Y-axis is vertical
• Perpendicular to vertical is horizontal
• Horizontal lines are parallel to x-axis

Step 5: Calculate the Distance

Now we need to find the distance between:

• Point A: (2, 3)
• Point B: (0, 3) [where the perpendicular meets y-axis]

Notice that both points have the same y-coordinate (3). They differ only in their x-coordinates.

The distance is simply: |2 – 0| = 2 units

Answer: 2 units (Option A)

The Beautiful Shortcut

Once you understand the concept, you don’t need to draw anything!

Distance of any point from y-axis = Absolute value of its x-coordinate

For point (2, 3):

• Distance from y-axis = |2| = 2 units
• Distance from x-axis = |3| = 3 units

This works for any point:

• Point (5, 7): Distance from y-axis = 5 units
• Point (-4, 2): Distance from y-axis = |-4| = 4 units
• Point (6, -3): Distance from x-axis = |-3| = 3 units

Why Students Get This Wrong

Despite being simple, some students choose wrong answers. Here’s why:

Mistake 1: Choosing Option B (3 units)

• They confuse distance from y-axis with distance from x-axis
• Remember: y-axis is vertical, so distance depends on horizontal displacement (x-coordinate)

Mistake 2: Choosing Option C (5)

• They simply add the x and y coordinate and might think that is the answer.

Mistake 3: Not understanding “shortest distance”

• Some students might think there are multiple distances
• Always remember: shortest distance to a line = perpendicular distance

Connecting to Other Topics

This simple concept connects to many advanced topics:

1. Distance Formula: When you need distance between two points not on the same horizontal/vertical line, you use: d = √[(x₂-x₁)² + (y₂-y₁)²]

2. Reflection: If you reflect (2, 3) about the y-axis, you get (-2, 3). Notice the distance from y-axis remains 2 units!

3. Section Formula: Understanding how coordinates work is essential for dividing line segments.

4. Area of Triangles: You often need perpendicular distances to calculate areas.

Quick Tips for Board Exams

1. Draw a diagram: Even if you know the shortcut, draw a quick sketch for 1-mark questions. It prevents silly mistakes.
2. Read carefully: “Distance from y-axis” vs “distance from x-axis” vs “distance from origin” are three different things!
3. Use absolute values: If the point is (-3, 5), distance from y-axis is |-3| = 3, not -3.
4. Verify with logic: Does your answer make sense visually? If the point is at x = 2, it should be 2 units from the y-axis (which is at x = 0).
5. Practice all four quadrants: Try points in different quadrants to cement the concept.

Practice Questions

Test your understanding:

1. Distance of (-5, 3) from y-axis = ? [Answer: 5 units]
2. Distance of (4, -7) from x-axis = ? [Answer: 7 units]
3. Distance of (-2, -3) from origin = ? [Answer: √13 units]

Remember: In board exams, these “easy” 1-mark questions are your scoring opportunities. Don’t overthink them, but don’t underestimate them either. A strong foundation in basics like this will help you tackle complex problems with confidence.

Keep practicing, keep visualizing, and keep understanding the “why” behind every concept. That’s the path to mastering mathematics!

Want more detailed solutions? Check out our complete video series on the CBSE Class 10 Sample Papers where we explain every question with crystal clarity.

Happy learning! 🎯📐