source: ncert
topic: geometry
class_level: class_9
chapter: ch3
difficulty: beginner
Class 9 | Ch3: Coordinate Geometry CARTESIAN PLANE: Two perpendicular lines: x-axis (horizontal) and y-axis (vertical). Origin O = (0,0). Point P = (x,y) where x=abscissa, y=ordinate. QUADRANTS: I: (+,+) — right of y-axis, above x-axis. II: (-,+) — left of y-axis, above x-axis. III: (-,-) — left of y-axis, below x-axis. IV: (+,-) — right of y-axis, below x-axis. Points ON axes: x-axis has y=0. y-axis has x=0. PLOTTING POINTS: Start at origin. Move right/left for x (positive=right, negative=left). Then move up/down for y (positive=up, negative=down). Mark the point. DISTANCE FORMULA (introduced here, developed in Class 10): Distance between A(x1,y1) and B(x2,y2) = sqrt((x2-x1)^2+(y2-y1)^2). COLLINEAR POINTS: three points lie on same straight line. SECTION FORMULA (for later): divides line segment in given ratio. GRAPHS OF LINEAR EQUATIONS: y=x: line through origin at 45°. y=-x: line through origin at 135°. x=a: vertical line. y=b: horizontal line. SOLVED EXAMPLES: Example 1: Plot A(3,4), B(-2,3), C(-4,-1), D(2,-3). A: Quadrant I (both positive). B: Quadrant II. C: Quadrant III. D: Quadrant IV. Example 2: Find distance between A(3,4) and B(-2,3). AB = sqrt((-2-3)^2+(3-4)^2) = sqrt(25+1) = sqrt(26) units. Example 3: In which quadrant is (-3,-5)? Both negative → Quadrant III. COMMON MISTAKES: Point (3,4) is NOT same as (4,3). First coordinate is always x (horizontal). Origin (0,0) is not in any quadrant — it's at the intersection of axes. Points on x-axis have y-coordinate=0, not x-coordinate=0.