4. The abscissa of a point is its perpendicular distance from y-axis.
5. The ordinate of a point is its perpendicular distance from x-axis.
6. The abscissa of every point situated on the right side of y-axis is positive and the abscissa of every point situated on the left side of y-axis is negative.
7. The ordinate of every point situated above x-axis is positive and that of every point below x-axis is negative.
8. The abscissa of every point on y-axis is zero.
9. The ordinate of every point on x-axis is zero.
10. The distance between any two points and is given by
11. If O(0, 0) is the origin and P(x, y) is any point then from the above formula, we have :
12. In order to prove that a given figure is a :
(i) square, prove that four sides are equal and the diagonals are equal.
(ii) rhombus, prove that the four sides are equal.
(iii) rectangle, prove the opposite sides are equal and the diagonals are also equal.
(iv) parallelogram, prove that the opposite sides are equal
(v) parallelogram but not a rectangle, prove that its opposite sides are equal but diagonals are not equal.
13. Three points A, B and C are said to be collinear, if they lie on the same straight line.
14. For three points to be collinear, the sum of the distances between two pairs of points is equal to the third pair of points.
15. Three points will make :
(i) a scalene triangle, if no two sides of the triangle are equal.
(ii) an isosceles triangle, if any two sides are equal
(iii) an equilateral triangle, if all the three sides are equal.
(iv) a right triangle, if sum of the squares of any two sides is equal to the square of the third side.
16. The coordinates of the point which divides the line segment joining and internally in the ratio , are given by :
17. The coordinates of the mid-point of a line segment with end points and are :
18. The point of intersection of the medians of a triangle is called its centroid.
19. The coordinates of the centroid of the triangle whose vertices are and are given by
20. The area of with vertices and is given by : area
Since area of a triangle cannot be negative we consider the absolute or numerical value of the area.
21. Three given points and are collinear if