Coordinate geometry · Year 12
In Year 12 you learn: equations of lines.
Coordinate geometry uses algebra to describe lines and circles. With the coordinates of points you can find gradients, midpoints and distances, write equations of lines, and spot parallel and perpendicular lines and circles.
Key facts
- Gradient m = (y₂ − y₁)/(x₂ − x₁); a straight line is y = mx + c.
- Parallel lines have equal gradients; perpendicular gradients multiply to −1.
- Midpoint ((x₁ + x₂)/2, (y₁ + y₂)/2); distance √((x₂ − x₁)² + (y₂ − y₁)²).
Worked examples
Example 1
Find the equation of the line through (1, 3) and (4, 9).
Answer: y = 2x + 1
Example 2
Find the equation of the line perpendicular to y = 3x − 2 that passes through (6, 1).
Answer: y = −(1/3)x + 3