Worked example 1
Find a median
Triangle ABC has A(0, 4), B(-2, 0) and C(4, 0). Find the median from A.
- The midpoint of BC is (1, 0).
- The gradient from A(0, 4) to (1, 0) is −4.
- Use the point A in a line equation.
Answer: y = −4x + 4
Higher Mathematics
Higher Maths Geometrical line problems
Practise geometrical line problems for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Use medians, altitudes, perpendicular bisectors and line intersections in coordinate geometry.
Before you start
- Find midpoint and gradient.
- Write a line equation from a point and gradient.
- Use perpendicular gradients.
Explanation
Coordinate geometry problems become straight-line problems after translating the geometric property. A median passes through a vertex and the opposite midpoint; an altitude is perpendicular to the opposite side.
A perpendicular bisector passes through a side's midpoint and has the negative reciprocal gradient.
Method and rules
- Median: vertex to midpoint of opposite side.
- Altitude: vertex through a line perpendicular to the opposite side.
- Perpendicular bisector: midpoint plus perpendicular gradient.
Worked examples
Worked example 2
Method check
What two properties define a perpendicular bisector?
- One property gives a point and one gives a gradient.
So: It passes through the midpoint and is perpendicular to the segment.
Watch out
- Using a side endpoint instead of its midpoint for a median.
- Using the same gradient instead of the perpendicular gradient.
- Finding the correct line property but using the wrong vertex.
Exam reminder
For geometrical line problems, show the defining equation or formula before simplifying. Check that every final value satisfies the original restrictions, interval or context.
Related Higher Maths topics
Continue with the methods that connect most closely to this topic.