Key Points

1. The gradient of the straight line joining the points (x1, y1) and (x2, y2) is given by:
gradient = y2 - y1 ⁄ x2 - x1

2. Two lines are parallel when their gradients are equal.

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:

Distance AB = √(x2 - x1)2 + (y2 - y1)2

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):

y - y1 ⁄ y2 - y1 = x - x1 ⁄ x2 - x1
or
y - y1 ⁄ x - x1 = y2 - y1 ⁄ x2 - x1


6. The equation of a circle with centre (h, k) and radius r is:

(x - h)2 + (y - k)2 = r2


When the centre is at the origin (0, 0), this simplifies to:

x2 + y2 = r2

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