## Revision Notes for Ch 7 Coordinate Geometry Class 10th Mathematics

**Coordinate Geometry**

**•**

*: The branch of Mathematics in which algebraic methods are used to solve geometrical problems is known as coordinate geometry.*

__Coordinate Geometry__**Coordinate System**

• As shown in the figure, the line XOX′ is known as the X-axis and YOY′ is known as Y-axis.

• The point O is called the origin. For any point P (x y), the ordered pair (x y) is called the

__coordinate__of point P.

• The distance of a point from Y-axis is called its

__abscissa__and the distance of a point from X-axis is called its

__ordinate__.

**• Distance between Two Points**

The distance between two points P (x

This is also known as

Note: The distance of any point P(x,y) from the origin O(0,0) is given by:

_{1}, y_{1}) and Q (x_{2}, y_{2}) is given by:This is also known as

__Distance Formula__.Note: The distance of any point P(x,y) from the origin O(0,0) is given by:

**• Section Formula**

Let P (x,y) be a point on the line segment joining A(x

_{1}, y_{1}) and B(x_{2}, y_{2}) such that it divides AB internally in the ratio m:n. The coordinates of the point P are given by
This is known as

__Section Formula__.
Note:

(i) If the point P divides the line segment joining A(x

_{1}, y_{1}) and B(x_{2}, y_{2}) internally in the ratio k:1, its coordinates are given by:**Example:**In what ratio does the point (2,- 5) divide the line segment joining the points A(-3, 5) and B(4, -9).

**Solution:**

Let the ratio be λ : 1

The required ratio is 5:2.

**Mid -Point Formula**

The mid-point of the line joining A(x

_{1}, y

_{1}) and B(x

_{2}, y

_{2}) is given as

**Centroid of the Triangle**

The Centroid of the triangle is the point of intersection of medians of the triangle. For a triangle A(x

_{1}, y

_{1}), B(x

_{2}, y

_{2}) and C(x

_{3}, y

_{3}) we can say that the co-ordinates of centroid is given as

**Areas of Triangle**

**Condition for Collinearity of three Points**