Class 9 Maths Cha 7 Coordinate Geometry Shorts | 🎯 99% Get This Wrong! Quadrant of (-1,-5) Revealed!

Описание: Welcome to our Mathematics Learning Hub 🎓✨!
In this video, we solve a very interesting MCQ from Coordinate Geometry:
👉 “In which quadrant does the point (-x, -y) lie?”

This may look like a small question, but to answer it correctly, we need to fully understand the concept of coordinate axes, quadrants, positive and negative values of x and y, and how points are plotted on a Cartesian plane. In this detailed description, we’ll explore all the basics of coordinate geometry, step-by-step quadrant rules, common mistakes students make, and more.

🌍 Introduction to Coordinate Geometry

Coordinate Geometry, also known as Analytical Geometry, is a branch of mathematics where we study the position of points, lines, and curves using a coordinate system. It forms the foundation of higher-level math, physics, engineering, and even computer graphics.

The system most widely used is the Cartesian Coordinate System, named after the French mathematician René Descartes. It uses two perpendicular number lines called:

X-axis (horizontal)

Y-axis (vertical)

The point where both axes intersect is called the origin (0,0). Every point in the plane is represented by an ordered pair (x, y), where x is the horizontal distance from the origin and y is the vertical distance.

🧭 Understanding Quadrants in the Cartesian Plane

The Cartesian plane is divided into four quadrants by the x-axis and y-axis. Each quadrant has a specific sign convention for x and y coordinates.

Here’s the breakdown:

1️⃣ First Quadrant

Both x and y are positive.

Example: (3, 4).

2️⃣ Second Quadrant

x is negative, y is positive.

Example: (-2, 5).

3️⃣ Third Quadrant

Both x and y are negative.

Example: (-1, -5).

4️⃣ Fourth Quadrant

x is positive, y is negative.

Example: (6, -2).

✅ Important Note: If either x = 0 or y = 0, the point lies on an axis, not in any quadrant.

📝 The Question: In Which Quadrant Does (-1, -5) Lie?

Let’s analyze the given point: (-1, -5)

x = -1 (negative)

y = -5 (negative)

From the quadrant rules, when both x and y are negative, the point lies in the Third Quadrant.

✔️ Correct Answer: Third Quadrant 🎯

🎯 Step-by-Step Solution Approach for MCQs

Check the sign of x-coordinate:

Positive → Right side of y-axis.

Negative → Left side of y-axis.

Check the sign of y-coordinate:

Positive → Above x-axis.

Negative → Below x-axis.

Match with quadrant rules:

(+, +) → 1st quadrant.

(-, +) → 2nd quadrant.

(-, -) → 3rd quadrant.

(+, -) → 4th quadrant.

For (-1, -5), both are negative, so clearly it belongs to the Third Quadrant.

⚡ Common Mistakes Students Make

Mixing quadrants: Many students confuse 2nd and 3rd quadrant because both have negative x-values. The difference is whether y is positive or negative.

Forgetting axis points: If x or y = 0, the point lies on an axis, not in any quadrant. Example: (0,5) is on the y-axis.

Plotting errors: Some students place negative values in the wrong direction. Always remember → left for negative x, down for negative y.

📚 Applications of Quadrants in Real Life

Coordinate geometry and quadrants aren’t just theoretical. They are used in:

Navigation & GPS systems (latitude & longitude coordinates).

Computer graphics & animations (every pixel has an (x, y) position).

Robotics & engineering (robot movement based on coordinates).

Physics & astronomy (tracking object positions).

Architecture & design (blueprints and CAD software).

Understanding quadrants is therefore a life skill beyond exams.

🔑 Important MCQs in Coordinate Geometry (with Answers)

Point (4, -3) lies in which quadrant? → Fourth Quadrant.

Point (-7, 2) lies in which quadrant? → Second Quadrant.

Point (-6, -9) lies in which quadrant? → Third Quadrant.

Point (0, 8) lies where? → On y-axis, not in any quadrant.

Point (9, 0) lies where? → On x-axis, not in any quadrant.

Appears in MCQs in Board Exams (Maths Class 9th, 10th, 11th, 12th).

Useful in SAT, GRE, GMAT and entrance tests.

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