A– LEVEL TOPIC REVIEW
unit C1 coordinate geometry
1. Write down the gradient and the coordinates of the intercept with the y–axis of the following lines:
a) / / b) / / c) / / d) / / (6 marks)2. Find the gradient of the straight line passing through:
a) / (2, 4) and (5, 16) / b) / (4, –5) and (2, –1)c) / (3, 5) and (5, 5) / d) / (4, 1) and (4, 7) / (4 marks)
3.Prove that the points A(4,0), B(7,–3), C(–2,–2) and D(–5,1) are the vertices of a parallelogram. (4 marks)
4.a) Find the equation of the line passing through the points P (1, 5) and Q (3, 9). (3 marks)
b)Calculate the point of intersection of the line PQ with the line . (3 marks)
5.a)Write down the equation of the line passing through (–2, 1) and parallel to the line . (3 marks)
b)Find the equation of the line passing through (3, –4) and perpendicular to the line , expressing your answer in the form , where a, b and c are integers to be found. (5 marks)
c) Sketch the line , indicating the intercepts on both axes. (2 marks)
6.a)Prove that the triangle with vertices at the points A (2, 1), B (4, 5) and C (0, 7) is right-angled. (4 marks)
b)Calculate the area of this triangle. (2 marks)
7. The points P (2, p) and Q both lie on the line whose equation is .
a) Calculate the values of p and q. (5 marks)
b) Calculate the distance between the points P and Q, in the form . (3 marks)
8.Find the equation of the perpendicular bisector of (2, –5) and (6, 9), expressing your answer in the form , where a, b and c are integers to be found. (6 marks)
A– LEVEL TOPIC REVIEW : ANSWERS
unit C1 coordinate geometry
1. a) 2; (0, 3) A1
b) –3; (0, 4) A1
c) M1
; A1
d) M1
; (0, –3) A1
2. a) A1
b) A1
c) A1
d) A1
3. gradients : AB = –1, CD = –1 M1
gradients : BC = grad DA = M1A1
two pairs of parallel sides A1
4. a) M1
A1
A1
b) solve simultaneous equations M1
(–8, –13) M1A1
5. a) M1
M1A1
b) M1A1
M1A1
A1
c) intercepts (0, 6), (8, 0) G2
6. a) either Pythagoras
M2A1
A1
or gradients : AB = 2, BC = M2A1
A1
b) M1A1
7. a) M1A1
M1A1
A1
b) M2A1
8. midpoint (4, 2) B1
M1A1
M1A1
A1