3. Two lines are perpendicular when the product of their gradient is -1.
4. When the points A and B have co-ordinates (x1, y1) and (x2, y2) respectively, then:
Mid-point of line AB is (x1 + x2 ⁄ 2, y1 + y2 ⁄ 2).
5. The equation of a straight line may take any of the following forms:
line parallel to the y axis: x = a
line parallel to the x acis: y = b
line through the origin with gradient m: y = mx
line through (0, c) with gradient m: y = mx + c
line through (x1, y1) with gradient m: y - y1 = m(x - x1)
line through (x1, y1) and (x2, y2):
6. The equation of a circle with centre (h, k) and radius r is:
When the centre is at the origin (0, 0), this simplifies to: