## Notes### Formulas#### 1. DistanceIf
*A* (
*x*_{1},
*y*_{1}) and
*B*(
*x*_{2},
*y*_{2},), then distance
*d*, from
*A* to
*B* =
#### 2. Midpoint#### 3. Gradient/Slope#### 4. Equation of a line
*y* =
*mx* + *c*
**y - y**_{1} = m(x - x_{1})#### 5. Parallel linesIf 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 (x _{1}, y _{1}), (x _{2}, y _{2}), (x _{3}, y _{3}) **8. Shoelace formula**
- go anti-clockwise direction
- must go back to first coordinate
#### 9. CircleThe 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
**x**^{2} + y^{2} = a^{2}The general equation of a circle is **x**^{2} + y^{2 }+ 2gx + 2fy + c = 0where the centre is (-g,-f) and radius is The equation of a circle whose one diameter is the line segment joining the points (x _{1}, y _{1}), (x _{2}, y _{2}) is given by (x - x _{1})(x - x _{2}) + (y - y _{1})(y - y _{2}) = 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 |