Some geometry questions can be solved by coordinates, by vectors or by a mixture. The skill is choosing one, saying why, and checking the answer against the picture.
This section is part of coordinate geometry. It assumes you know gradient, midpoint and distance from that chapter.
What do the four lessons cover?
Choosing a coordinate method rather than a vector method teaches how to pick a method and write the reason. Recovering a parameter when a line touches a curve links geometry to the discriminant.
Checking an algebraic intersection against a geometric restriction teaches you to reject answers that break a condition. Writing a complete geometric argument when a diagram is not to scale covers reasons that do not depend on the picture.
How can two methods give the same answer?
Here is an original example. Find the point P on AB with AP : PB = 1 : 2, where A(2, 1) and B(8, 7).
By coordinates, P = ((2 × 2 + 1 × 8) ÷ 3, (2 × 1 + 1 × 7) ÷ 3) = (4, 3). By vectors, AB = (6, 6), so P = A + ⅓AB = (2, 1) + (2, 2) = (4, 3).
Both give (4, 3). If the next part asks for the equation of a line through P, the coordinate method already has the point ready, and that wording is the reason to prefer it.
Where should you start?
- Choosing a method is unclear: begin with the lesson on choosing a coordinate method.
- Answers sometimes break a condition: go to the lesson on checking an intersection against a restriction.
- Close to an exam: use the geometry problems practice set and the word-problem structure worksheet.
When is tuition worth considering?
Free lessons show each method. A one-to-one teacher listens to why you chose a method and tells you whether the reason would earn the mark.
Read online one-to-one SPM Additional Mathematics tuition for an example lesson, or return to the coordinate geometry guide.