C12 Coordinate Geometry (I)
对应大纲的内容
| M4.9 | Work with coordinates in all four quadrants. |
| M4.10 | Identify and interpret gradients and intercepts of linear functions ($y = mx + c$) graphically and algebraically.
Identify pairs of parallel lines and identify pairs of perpendicular lines, including the relationships between gradients. Find the equation of the line through two given points, or through one point with a given gradient. |
| M5.10 | Solve geometrical problems on 2‑dimensional coordinate axes. |
| M5.19 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors.
Use vectors to construct geometric arguments and proofs. |
学习目标
- Master coordinate projections by calculating exact distances, midpoints, and precise ratio-divisions of line segments (e.g., finding point $P$ that divides $A B$ in ratio $\lambda: 1$ ) across all four Cartesian quadrants.
- Synthesise linear architectures by translating fluently between gradient-intercept $(y=m x+c)$, point-gradient ( $y-y_1=m\left(x-x_1\right)$ ), and general forms $(a x+b y+c=0)$ to identify intercepts and gradients instantly.
- Exploit orthogonal constraints by rigorously applying parallel $(m_1=m_2)$ and perpendicular $(m_1 m_2=-1)$ gradient axioms to construct geometric bounds, calculate shortest distances, and execute point-reflection transformations.
建议时间
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 8 | 120 min |
| Quiz | 7 | 20 min |
| Practice A | 30 | 50 min |
| Practice B | 22 | 50 min |
| Total | 67 | approx. 4-5 hrs |
