OCR Advanced FSMQ - Additional Maths

2 Find the gradients of the lines joining each of the following pairs of points: (a) (2, 3) and (4, 9) (b) (1, 0) and (9, 12) (c) (−2, 3) and (−5, 0) (d) (−1, 10) and (−5, 1) (e) (0, −3) and (1, 6) (f) (1, −2) and (4, 2) (g) (10, −4) and (−1, −5) 3 Find the coordinates of the mid-point of the lines joining the following points: (a) (1, 2) and (3, 8) (b) (0, 2) and (4, 1) (c) (−2, 5) and (0,−5) (d) (−8, 4) and (−2, −6) (e) (10, 12) and (−3, 0) (f) (−3, −4) and (−4, 6) (g) (8, −1) and (−5, 7) 4 Find the lengths of the lines joining the following points, giving each answer to three significant figures: (a) (1, 5) and (5, 9) (b) (3, 4) and (6, 9) (c) (1, 0) and (6, 12) (d) (−3, 2) and (2, 6) (e) (−5, 0) and (0, 4) (f) (−12, 5) and (0, 10) (g) (−6, −3) and (−7, 2) 5 Using vectors, show that the following pairs of lines are the same length: (a) AB where A and B are the points (0, 5) and (3, 4) respectively. CD where C and D are the points (5, 6) and (8, 5) respectively. (b) AB where A and B are the points (0, 1) and (5, 2) respectively. CD where C and D are the points (0, −1) and (5, 0) respectively. (c) AB where A and B are the points (−2, −3) and (4, −4) respectively. CD where C and D are the points (−6, −5) and (0, −6) respectively. (d) AB where A and B are the points (0, 10) and (6, 9) respectively. CD where C and D are the points (2, 7) and (8, 8) respectively. (e) AB where A and B are the points (8, 0) and (6, 4) respectively. CD where C and D are the points (9, −1) and (5, −3) respectively. (f) AB where A and B are the points (0, −7) and (6, −6) respectively. CD where C and D are the points (−3, 1) and (−2, 7) respectively. (g) AB where A and B are the points (−1, 0) and (0, 2) respectively. CD where C and D are the points (2, 2) and (4, 3) respectively. 6 Using the distance formula √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 for the distance between two points, calculate the lengths of the following lines, giving your answers to three significant figures: (a) AB where A is (1, 4) and B is (6, 7). (b) CD where C is (0, 5) and D is (5, 17). (c) EF where E is (−1, −5) and F is (−3, 0). (d) GH where G is (4, −1) and H is (2, 4). 6 Coordinate geometry of straight lines 127