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Class 9 Orienting Yourself: The Use of Coordinates: cheat sheet
CBSE Mathematics. Every point in a plane is fixed by two numbers (x, y). From the coordinates we can find quadrants, distances, midpoints and reflections.
Key ideas
- The x-axis and y-axis meet at right angles at the origin O (0, 0). The x-coordinate is always written first.
- Quadrants go anticlockwise from the top right: I (+, +), II (−, +), III (−, −), IV (+, −).
- A point with y = 0 lies on the x-axis; a point with x = 0 lies on the y-axis.
- Points with the same y-coordinate lie on a line parallel to the x-axis; with the same x-coordinate, parallel to the y-axis.
- Reflect in the x-axis: the y-coordinate changes sign. In the y-axis: the x-coordinate changes sign. In the origin: both change sign.
- Use the distance formula to test whether three points form an isosceles, right-angled or equilateral triangle.
Remember
| Distance between two points | d = √((x₂ − x₁)² + (y₂ − y₁)²) |
| Distance from the origin | d = √(x² + y²) |
| Midpoint | ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Same x (vertical distance) | d = difference of the y-coordinates |
Watch out
- Writing (y, x) instead of (x, y): (2, 5) and (5, 2) are different points.
- Dropping a minus sign when squaring: (−3)² = 9, not −9.
- Forgetting the square root at the end of the distance formula.
Worked example
Say where each point lies: (3, 9), (8, 6), (−6, 4), (7, 6).
Working: I (+, +), II (−, +), III (−, −), IV (+, −); a 0 puts the point on an axis
Answer: quadrant I; quadrant I; quadrant II; quadrant I
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