Coordinate Geometry is like giving addresses to points in space! In "Chapter 3: Coordinate Geometry," you will learn how to locate points on a plane using numbers and how to find the distance and area between them.

What is Coordinate Geometry?

Coordinate Geometry, also called Cartesian Geometry, combines algebra and geometry. It helps you describe the position of a point using an ordered pair of numbers called coordinates.

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Cartesian Plane

The Cartesian plane is a flat surface with two number lines:
X-axis: Horizontal line.
Y-axis: Vertical line.

These two axes meet at a point called the origin.

The plane is divided into four parts, called quadrants:

First Quadrant: Both horizontal and vertical values are positive.
Second Quadrant: Horizontal value is negative, vertical value is positive.
Third Quadrant: Both horizontal and vertical values are negative.
Fourth Quadrant: Horizontal value is positive, vertical value is negative.

Coordinates of a Point

The coordinates of a point show:

How far the point is from the vertical line.
How far the point is from the horizontal line.

Example: A point with positive horizontal and positive vertical values lies in the first quadrant.

Plotting Points

To plot a point:
Start at the origin.
Move along the horizontal line by the horizontal value.
From there, move parallel to the vertical line by the vertical value.
Mark the point.

Finding Distance Between Two Points

The distance between two points can be found by using the differences between their horizontal and vertical values. It is similar to applying the Pythagoras theorem to a right-angled triangle formed between the two points.

Sectioning a Line Segment

If you want to find the point that divides a line between two points in a certain ratio, you use the sectioning method. It gives the exact spot depending on the given ratio.
When the ratio is equal, the division point is exactly halfway between the two points.

Area of a Triangle Formed by Three Points

You can find the area of a triangle formed by three points by using a method based on their horizontal and vertical values. If the area comes out to be zero, it means the three points are in a straight line.

Important Notes

The sign of the coordinates is very important when placing points.
Distance from a point to the origin can be found by treating the origin's values as zero.
If two points have the same horizontal value, the line between them is vertical.
If two points have the same vertical value, the line between them is horizontal.

Real-life Applications

Coordinate Geometry is used in:
Mapping locations on Earth.
Designing video games and animations.
Construction, architecture, and engineering projects.
Astronomy to map stars and planets.
GPS tracking and navigation.

Top 10 FAQs about Coordinate Geometry

Q1. What are coordinates?
Coordinates are a pair of numbers that show the position of a point on the Cartesian plane.

Q2. What is the Cartesian plane?
It is a flat surface made up of a horizontal line and a vertical line that cross at a starting point called the origin.

Q3. What are quadrants?
The Cartesian plane is divided into four sections called quadrants.

Q4. How do you find the distance between two points?
By comparing the differences in their horizontal and vertical values and applying the idea of a right-angled triangle.

Q5. What is the midpoint between two points?
It is the point that lies exactly halfway between two points.

Q6. What does the section method do?
It helps find a point that divides a line joining two points into a given ratio.

Q7. How is the area of a triangle found using coordinates?
By using the horizontal and vertical values of the three vertices in a special formula.

Q8. What does it mean if the area of a triangle is zero?
It means the points are collinear, lying on a straight line.

Q9. Why are signs important in coordinates?
Signs tell you which direction to move from the origin and which quadrant the point lies in.

Q10. How is coordinate geometry used in daily life?
It is used in mapping, GPS systems, construction designs, game development, and more.