Coordinate geometry · Grade 11

In Grade 11 you learn: equations of circles.

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).
• Circle with centre (a, b) and radius r: (x − a)² + (y − b)² = r².
• A tangent to a circle is perpendicular to the radius at that point.

Worked examples

Other years

• Coordinate geometry · Grade 9
• Coordinate geometry · Grade 10