Chapter 3 · Mathematics
Coordinates: Chapter Introduction
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Two numbers pin any seat in an exam hall, and any point on a plane: coordinates turn geometry into numbers.
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PDF, 173 KB · fill in the blanks, true/false, assertion-reason, MCQ, numericals, short answer, match the columns; detailed solutions at the end That's all the videos in this chapter so far Back to Coordinate Geometry
Key points
- Two perpendicular number lines, the x-axis and y-axis, meet at the origin O (0, 0).
- A point is an ordered pair (x, y): x along the x-axis, then y parallel to the y-axis.
- The axes split the plane into four quadrants: I (+, +), II (−, +), III (−, −), IV (+, −).
- Distances follow from numbers: (1, 1) to (4, 5) has legs 3 and 4, so the distance is 5.
Plotting a point
- Start at O (0, 0).
- Move x units along the x-axis (right if positive, left if negative).
- Then move y units parallel to the y-axis (up if positive, down if negative).
(3, 2): 3 right, then 2 up
Quadrants
| Quadrant | Signs | Example |
|---|---|---|
| I | (+, +) | (3, 2) |
| II | (−, +) | (−2, 4) |
| III | (−, −) | (−1, −3) |
| IV | (+, −) | (5, −2) |
Distance without a ruler
(1, 1) → (4, 5): horizontal 3, vertical 4, distance = √(3² + 4²) = 5
Try it yourself
Goal: Place points by their coordinates, see what the signs and the order do, and find distances from the numbers alone.
- Tap the plane or use the sliders to move P, and watch the walk from O.
- Press Swap x and y to compare the two points.
- Add a second point and read the distance from the two legs.
- Press Plot this point and place the coordinates you are given.
Quick quiz
4 questions. Choose an answer for each, then submit to see your score and the explanations.