OCR Advanced FSMQ - Additional Maths

y x A B 1 0 1 2 2 3 3 4 5 5 6 6 4 4 2 To prove that two lines are the same length it is only necessary to show that the two vectors representing the lines are the same. It does not matter if the x and the y are swapped around nor does it matter about the signs. The following vectors are equal in length. ( 3 2 ) and ( 2 3 ) ( −1 4 ) and ( 1 −4 ) ( −3 2 ) and ( −2 3 ) Example 2 Using vectors, show that the following pairs of lines are the same length. AB where A and B are the points (0, 5) and (2, 2) respectively. CD where C and D are the points (3, 1) and (6, 3) respectively. Answer 2 Here we have drawn the lines AB and CD on a grid. The vector to go from A to B is ( 2 –3 ) because you go two squares to the right and three down. The vector to go from C to D is 3 2 because you go three squares to the right and two up. What you are doing here is showing that the two sides that are either side of the right angle are the same size for both triangles formed. The length of the hypotenuse of each triangle will be equal. It is not necessary to find the length of the hypotenuse if you only have to prove that two lines are equal length. 6 Coordinate geometry of straight lines 121