Notes

📘 Coordinate Geometry Class 10 Notes (Chapter 7)

🔷 Introduction

Coordinate geometry is an important branch of mathematics. In simple words, it helps us locate points on a plane using numbers. This chapter combines algebra and geometry. Therefore, students can solve geometric problems using formulas and coordinates.

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🔷 Cartesian Plane

The coordinate plane was developed by René Descartes. Hence, it is also called the Cartesian plane.

It consists of two perpendicular number lines:

• X-axis → Horizontal line
• Y-axis → Vertical line

These axes intersect at a point called the origin.

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🔷 Origin

The point where both axes meet is called the origin.

Coordinates of origin:$$(0,0)$$(0,0)

Thus, the origin acts as the starting point of the graph.

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🔷 Coordinates of a Point

A point on the graph is represented as:$$(x,y)$$(x,y)

Where:

• x-coordinate → Distance from y-axis
• y-coordinate → Distance from x-axis

For example:$$(4,3)$$(4,3)

Here:
x = 4
y = 3

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🔷 Terms Used in Coordinate Geometry

✔ Abscissa

The x-coordinate of a point is called the abscissa.

Example:

In (5,2), abscissa = 5

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✔ Ordinate

The y-coordinate of a point is called the ordinate.

Example:

In (5,2), ordinate = 2

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🔷 Quadrants

The x-axis and y-axis divide the plane into four parts called quadrants.

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First Quadrant

$$(+,+)$$(+,+)

Both x and y are positive.

Example:$$(3,4)$$(3,4)

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Second Quadrant

$$(-,+)$$(−,+)

x is negative and y is positive.

Example:$$(-2,5)$$(−2,5)

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Third Quadrant

$$(-,-)$$(−,−)

Both x and y are negative.

Example:$$(-3,-4)$$(−3,−4)

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Fourth Quadrant

$$(+,-)$$(+,−)

x is positive and y is negative.

Example:$$(4,-2)$$(4,−2)

Therefore, the signs of coordinates help us identify the quadrant.

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🔷 Position of Points on Axes

Point on x-axis

If y = 0, the point lies on x-axis.

Example:$$(5,0)$$(5,0)

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Point on y-axis

If x = 0, the point lies on y-axis.

Example:$$(0,7)$$(0,7)

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Origin

If x = 0 and y = 0:$$(0,0)$$(0,0)

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🔷 Important Observations

• A point in first quadrant has positive coordinates.
• A point in third quadrant has negative coordinates.
• Any point on x-axis has ordinate = 0.
• Any point on y-axis has abscissa = 0.

As a result, identifying points becomes much easier.

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🔷 Real-Life Applications

Coordinate geometry is used in:

• Maps and navigation
• Video games
• Engineering designs
• Architecture
• Computer graphics
• GPS systems

Thus, coordinate geometry is useful in everyday life.

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