Coordinate Geometry –

📘 Coordinate Geometry – Short Notes

👨‍🏫 Introduction

• (1637) introduced the Cartesian coordinate system.
• This led to the development of coordinate geometry.

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📐 What is Coordinate Geometry?

• A branch of mathematics where geometry is solved using algebra with the help of coordinates.

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📊 Coordinate System

🔹 Coordinate Axes

• Two perpendicular lines:
  • x-axis → horizontal line
  • y-axis → vertical line
• Intersection point = Origin (O)

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🔹 Cartesian Plane

• The plane formed by x-axis and y-axis.

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➕ Convention of Signs

• Right side of origin → + (positive x)
• Left side → – (negative x)
• Upward → + (positive y)
• Downward → – (negative y)

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🔢 Ordered Pair

• Written as (x, y)
• Example:
  • (2, 3) ≠ (3, 2)

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📍 Coordinates of a Point

• Point P(a, b):
  • a = x-coordinate (abscissa)
  • b = y-coordinate (ordinate)

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🧭 Quadrants

Quadrant	Sign of (x, y)
I	(+, +)
II	(–, +)
III	(–, –)
IV	(+, –)

👉 Axes divide plane into 4 quadrants

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⚠️ Important Notes

• Points on x-axis → (x, 0)
• Points on y-axis → (0, y)
• Origin = (0, 0)
• Points on axes do not belong to any quadrant

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📏 Distance Between Two Points

👉 Distance between A(x₁, y₁) and B(x₂, y₂)

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📏 Distance from Origin

👉 Distance of point P(x, y) from origin

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✏️ Examples

Example 1:

A(7, 13), B(10, 9)

Distance = √[(10−7)² + (9−13)²]
= √(9 + 16) = √25 = 5 units

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Example 2:

P(-4, 7), Q(2, -5)

Distance = √[(2+4)² + (-5−7)²]
= √(36 + 144) = √180 = 6√5