CBSE Class 10 Mathematics Coordinate Geometry Notes Set A

CBSE Class 10 Mathematics - Coordinate Geometry Concepts. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Class-X

Chapter 7: Coordinate Geometry

Top Definitions

1. Two perpendicular number lines intersecting at point zero are called coordinate axes. The horizontal number line is the x-axis (denoted by X’OX) and the vertical one is the y-axis (denoted by Y’OY).

2. The point of intersection of x axis and y axis is called origin and denoted by ‘O’.

3. Cartesian plane is a plane obtained by putting the coordinate axes perpendicular to each other in the plane. It is also called coordinate plane or xy plane.

4. The x-coordinate of a point is its perpendicular distance from y axis.

5. The y-coordinate of a point is its perpendicular distance from x axis.

6. The point where the x axis and the y axis intersect is coordinate points (0, 0).

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

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

9. If the abscissa of a point is x and the ordinate of the point is y, then (x, y) are called the coordinates of the point.

Top Concepts

1. The axes divide the Cartesian plane into four parts called the quadrants (one fourth part), numbered I, II, III and IV anticlockwise from OX.

2. The coordinate of a point on the x axis are of the form (x,0) and that of the point on y axis are (0,y)

3. Sign of coordinates depicts the quadrant in which it lies. The coordinates of a point are of the form (+, +) in the first quadrant, (-, +) in the second quadrant, (-,-) in the third quadrant and (+,-) in the fourth quadrant.

4. Three points A, B and C are collinear if the distances AB, BC, CA are such that the sum of two distances is equal to the third.

5. Three points A, B and C are the vertices of an equilateral triangle if the distances AB = BC = CA.

6. The points A, B and C are the vertices of an isosceles triangle if the distances AB = BC or BC = CA or CA = AB.

7. Three points A, B and C are the vertices of a right triangle if AB² + BC² = CA² .

8. For the given four points A, B, C and D

(i) AB = BC = CD = DA; AC = BD ⇒ ABCD is a square.

(ii) AB = BC = CD = DA; AC ≠ BD ⇒ ABCD is a rhombus.

(iii) AB = CD, BC = DA; AC = BD ⇒ ABCD is a rectangle.

(iv) AB = CD, BC = DA; AC ≠ BD ⇒ ABCD is a parallelogram.

9. Diagonals of a square, rhombus, rectangle and parallelogram always bisect each other.

10. Diagonals of rhombus and square bisect each other at right angle.

11. Four given points are collinear, if the area of quadrilateral is zero.

12. Centroid is the point of intersection of the three medians of a triangle.

13. Centroid divides the median in the ratio of 2:1.

14. The incentre is the point of intersection of internal bisector of the angles. It is also the centre of the circle touching all the sides of a triangle.

15. Circum centre is the point of intersection of the perpendicular bisectors of the sides of the triangle.

16. Ortho centre is the point of intersection of perpendicular drawn from the vertices on opposite sides (called altitudes) of a triangle and can be obtained by solving the equations of any two altitudes.

17. If the triangle is equilateral, the centroid, incentre, orthocentre, circum centre coincides.

18. If the triangle is right angled triangle, then orthocentre is the point where right angle is formed.

19. If the triangle is right angled triangle, then circumcentre is the midpoint of hypotenuse.

20. Orthocentre, centroid and circum centre are always collinear and centroid divides the line joining Orthocentre and circumcentre in the ratio of 2:1.

21. In an isosceles triangle centroid, orthocentre, incentre, circumcentre lies on the same line.

22. Angle bisector divides the opposite sides in the ratio of remaining sides.

23. Three given points are collinear, if the area of triangle is zero.

Top Formulae

Top Diagrams

1. Sign of coordinates in various coordinates.

2. To plot a point P (3, 4) in the Cartesian plane.

(i) A distance of 3 units along X axis.

(ii) A distance of 4 units along Y axis.

3. Area of quadrilateral ABCD = Area of ΔABC + Area of ΔACD

4. Centroid (G) of a triangle.

5. Incentre (I) of a triangle.

6. Circumcentre (O) of a Triangle.

7. Orthocentre (O) of a Triangle.

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