# NCERT Class 10 Mathematics Coordinate Geometry CBSE Board Sample Problems

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## Coordinate Geometry

Flash Back from Class IX notes

1. We require two perpendicular axes to locate a point in the plane. One of them is horizontal and other is Vertical

2. The plane is called Cartesian plane and axis are called the coordinates axis

3. The horizontal axis is called x-axis and Vertical axis is called Y-axis

4. The point of intersection of axis is called origin.

5. The distance of a point from y axis is called x -coordinate or abscissa and the distance of the point from x -axis is called y -coordinate or Ordinate

6. The x-coordinate and y -coordinate of the point in the plane is written as (x, y) for point and is called the coordinates of the point

7. The Origin has zero distance from both x-axis and y-axis so that its abscissa and ordinate both are zero. So the coordinate of the origin is (0,0)

8. A point on the x -axis has zero distance from x-axis so coordinate of any point on the x-axis will be (x, 0)

9. A point on the y -axis has zero distance from y-axis so coordinate of any point on the y-axis will be (0, y)

10. The axes divide the Cartesian plane in to four parts. These Four parts are called the quadrants

11. The coordinates of the points in the four quadrants will have sign according to the below table

Quadrant | x-coordinate | y-coordinate |

1^{st} Quadrant | + | + |

2^{nd} quadrant | - | + |

3^{rd} quadrant | - | - |

4^{th} quadrant | + | - |

Quadrant |

Distance formula

Distance between the points AB is given by

D

Distance of Point A from Origin

**Section Formula**

A point , which divide the line segment AB in the ratio and is given by

The midpoint P is given by

**Area of Triangle ABC**

Area of triangle ABC of coordinates and

For point A, B and C to be collinear, the value of A should be zero