OCR Advanced FSMQ - Additional Maths

y x C D A B 1 0 1 2 2 3 3 4 5 5 6 6 4 > > >  TIP You may see examination questions referring to a line segment. A line segment is part of a line. Usually you will be given the coordinates of the point where the line segment starts and the coordinates where it finishes. Using these coordinates you can find the mid-point of the line segment or the length of the line segment. Vectors ( 2 –3 ) and ( 3 2 ) have the same length, so AB and CD are the same length. 6.4 Finding the mid-point of a straight 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 mid-point of the line joining the two points with coordinates (2, 6) and (8, 4) is ( 2 + 8 2 , 6 + 4 2 ) = (5, 5) Example 3 Find the mid-point and the gradient of the line joining the two points A  (−2, 0) and B  (6, 10). Answer 3 The mid-point of the line joining the two points with coordinates (−2, 0) and (6, 10) is −2 + 6 2 , 0 + 10 2 = (2, 5) Note that sometimes the word ‘line’ is used. A line is always a straight line. 2 Coordinate geometry 122