0Class 10 Mathematics – Coordinate Geometry Notes
1. Introduction
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Coordinate Geometry (also called analytical geometry) studies geometric figures using coordinates on a plane.
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It combines algebra and geometry to locate points and analyze shapes.
2. Coordinate Plane
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A flat surface divided into four quadrants by two lines:
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X-axis: horizontal line
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Y-axis: vertical line
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The intersection point of X-axis and Y-axis is called the origin.
3. Coordinates of a Point
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A point in the plane is represented as (x, y):
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x-coordinate: distance from the Y-axis (horizontal position)
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y-coordinate: distance from the X-axis (vertical position)
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Positive or negative signs indicate the quadrant where the point lies.
4. Quadrants
| Quadrant | x-coordinate | y-coordinate |
|---|---|---|
| 1st | + | + |
| 2nd | − | + |
| 3rd | − | − |
| 4th | + | − |
5. Plotting a Point
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Start at the origin.
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Move along the X-axis according to the x-coordinate.
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Move vertically according to the y-coordinate.
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Mark the point.
6. Distance Between Two Points (Conceptual)
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Distance is the length of the line segment connecting two points.
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The farther apart the points, the larger the distance.
7. Midpoint of a Line Segment (Conceptual)
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Midpoint is the point exactly in the middle of two points.
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It divides the line segment into two equal parts.
8. Collinearity of Points
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Collinear points lie on the same straight line.
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If three points are collinear, one point lies between the other two.
9. Applications of Coordinate Geometry
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Determining distances between points
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Finding midpoints of line segments
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Checking if points are collinear
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Representing geometric figures like triangles, rectangles, and squares on the plane
10. Important Points to Remember
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Always identify the quadrant using the signs of coordinates.
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Origin (0,0) belongs to no quadrant.
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Distance and midpoint help in analyzing geometric shapes mathematically.
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Coordinate geometry bridges algebra and geometry, making problem-solving easier.
