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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. |