The big picture
Most questions here need one measurement and a careful count.
| Idea | Remember | Example |
|---|---|---|
| The pair | First number across, second up, from the origin. | (3, 4) and (4, 3) are different places. |
| The quadrant | Two signs pick the region. A zero means an axis. | (6, 0) sits on the horizontal axis. |
| A shared coordinate | One subtraction. Never negative. | (2, 5) to (9, 5) is 7. |
| The distance | Square both gaps, add, then undo the square. | (2, 1) to (8, 9) is 10. |
| The midpoint | Average each coordinate on its own. | (2, 3) and (8, 11) meet at (5, 7). |
| Three in a line | The two hops cross-multiply to equal products. | (1, 2), (3, 6), (6, 12): 12 = 12. |
| A square corner | Two squared sides add to the third. | 16 + 9 = 25 at (4, 0). |
| The name | Sides, diagonals and midpoints, together. | Diagonals that halve each other: a parallelogram. |
| A mirror | In the y-axis, (x, y) goes to (−x, y). In the x-axis, (x, y) goes to (x, −y). Lengths stay the same. | (5, 2) in the y-axis is (−5, 2). |
| Against a circle | Compare x² + y² with r². Less is inside, equal is on, more is outside. | (3, 4) against r = 5: 25 = 25, so on. |
This is Chapter 1 in your NCERT book. It is called Orienting Yourself: The Use of Coordinates.
Four corners are eight numbers. A short list of checks then names the shape. Any two people working from those numbers reach the same answer.