Class 9 Maths

1.1 Why we need coordinates One number fixes a point on a line; a point in a plane needs two, measured along perpendicular axes. 1.2 Reading the plane The axes, the origin and the ordered pair (x, y). The x-coordinate is the distance from the y-axis. 1.3 Quadrants and signs Four quadrants, four sign patterns. (3, 5) and (5, 3) are different points, and reflection changes one sign. 1.4 Distance between two points The coordinate differences are the legs of a right triangle, and the Baudhayana-Pythagoras theorem gives the distance. 1.5 Midpoints and dividing a segment The midpoint is the average of the coordinates. The same idea finds a missing endpoint and the trisection points. 1.6 Coordinates in the real world Widths, overlaps of circles and collinearity, all calculated from coordinates on floor plans, grids and screens.