## Notes

### Formulas

#### 1. Distance

If A ( x1, y1) and B( x2, y2,), then distance d, from A to B

#### 4. Equation of a line

y = mx + c

y - y1 = m(x - x1)

#### 5. Parallel lines

If two lines are parallel, then they have the same gradient.

#### 6. Perpendicular lines

If two lines are perpendicular, then the product of the gradients of the two lines is -1.

or: perpendicular gradient = -1/m    where m is the gradient of the line perpendicular to it.

#### 7. Area of triangle

The area of the triangle formed by the three points (x1, y1), (x2, y2), (x3, y3)

#### 8. Shoelace formula

• go anti-clockwise direction
• must go back to first coordinate

#### 9. Circle

The equation of a circle whose center is (h,k) and radius is a is given by the equation

(x - h)2 + (y - k)2 = 0

The equation of a circle whose centre is the origin and whose radius is a is given by the equation

x2 + y2 = a2

The general equation of a circle is

x2 + y2 + 2gx + 2fy + c = 0

where the centre is (-g,-f) and radius is

The equation of a circle whose one diameter is the line segment joining the points
(x1, y1), (x2, y2) is given by

(x - x1)(x - x2) + (y - y1)(y - y2) = 0

### Example

1. Find the equation of the line with gradient 2 passing through (1, 4).

y - 4 = 2(x - 1)
y - 4 = 2x - 2
y = 2x + 2