OCR Advanced FSMQ - Additional Maths

Topic summary There are many formulae to remember in this topic and the best way to do this is by usage. This means that you should try to remember them as you are attempting any questions. If you forget a formula you may be able to work out the answer by drawing a diagram. Many coordinate geometry questions in the examination are similar and you usually require use of most of the material summarised here to answer a single question. It is also important to note that this is a very important topic because as well as being asked to answer whole questions on coordinate geometry, the content of this topic can crop up in parts of questions on other topics. The gradient of the line joining two points The gradient of the line joining points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by: Gradient = y 2 − y 1 x 2 − x 1 The length of a line joining two points The length of a straight line joining the two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by: √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 The mid-point of the line joining two points The mid-point of a line joining the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by: ( x 1 + x 2 2 , y 1 + y 2 2 ) The equation of a straight line The equation of a straight line with gradient m and which passes through a point ( x 1 , y 1 ) is given by: y − y 1 = m ( x − x 1 ) Condition for two straight lines to be parallel to each other The lines must both have the same gradient. Condition for two straight lines to be perpendicular to each other If one line has a gradient m 1 and the other a gradient of m 2 then m 1 m 2 = −1 if the lines are perpendicular to each other. 2 Coordinate geometry 142