Straight Lines and Triangle Geometry
Combine gradients and line equations with parallel, perpendicular, median, altitude and perpendicular-bisector properties.
How to study Higher Mathematics
Practise a skill without a calculator first, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and interpretation.
Core concepts
Concept 1
line equation
Exam cue: Which point and gradient define the required line?
Concept 2
parallel gradients
Exam cue: Is the line a median, altitude or perpendicular bisector?
Concept 3
perpendicular gradients
Exam cue: What angle convention is being used?
Concept 4
m = tan θ
Concept 5
triangle lines
Risk pitfalls and guardrails
Using a midpoint for an altitude
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Taking the negative but not reciprocal perpendicular gradient
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Reporting the calculator arctan value without choosing the correct line angle
Guardrail: Keep exact values through intermediate work and round only the final requested result.
Memory anchors
Parallel shares m
Non-vertical parallel lines have the same gradient.
Perpendicular multiplies to −1
Use the negative reciprocal when both gradients are defined.
Median meets midpoint
A median joins a vertex to the opposite side’s midpoint.
Altitude is perpendicular
An altitude passes through a vertex at right angles to the opposite side.
Bisector needs midpoint and right angle
A perpendicular bisector uses both properties.
Gradient meets angle
Use m = tan θ with the stated angle convention.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Find the gradient of the line through (2,3) and (6,11).
Find the equation of the line with gradient 3 through (2,−1).
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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