Revision questions


9A Core skills 1. A is the point (–6, 7) and B is the point (8, 0). (i) Find the midpoint of AB . (ii) Find |AB| . Give your answer in surd form. (iii) Find the slope of the line AB .


2. (i) Plot the points P ( 2, 1 ) and Q ( 6, 5 ) on a Cartesian plane. Join the points to form the line [PQ] .


(ii) Using your knowledge of constructions from Linking Thinking 1, construct the perpendicular bisector of the line PQ .


(iii) From your graph, what are the coordinates of M , the midpoint of [PQ] ?


(iv) Use the midpoint formula to confi rm your answer to (iii) above.


(v) Use the length of a line formula to verify that the line you constructed in (ii) bisects [PQ] .


3. (i) Plot the points X ( 4, 2 ) , Y ( 8, 0 ) and Z ( 6, −4 ) . (ii) Verify that the triangle XYZ is isosceles.


(iii) Using the converse of Pythagoras’s theorem, determine if this triangle is right-angled. Justify your answer using mathematical calculations.


4. (i)


Plot the points H ( 2, 3 ) , I ( −1, 5 ) , J ( −2, 0 ) and K ( 1, −2 ) .


(ii) Investigate if |HK| = |IJ| . (iii) Verify |HI| = |JK| .


(iv) Find the midpoint of [HJ] and show that it is also the midpoint of [IK] .


(v) What type of shape is HIJK ? Justify your answer.


5. The pointsA andB have coordinates (5, –1) and (13, 11) respectively.


(i) Find the coordinates of the midpoint of AB .


(ii) Given that AB is a diameter of the circle C, fi nd the length of the radius of the circle C . Give your answer in surd form.


6. The points P, Q, R and S have the coordinates (1, 10), (5, 2), (11, 5) and (13, 1), respectively.


Investigate whether the lines PQ and RS are parallel.


Section A Applying our skills 173 O A B


7. The points R, S, T and U have the coordinates (11, 5), (13, 1), (14, 4) and (2, –2), respectively.


Show that the lines RS and TUare perpendicular.


8. Using coordinate geometry calculations, show that the points A ( −2, 2 ) , B ( 1, 4 ) , C ( 2, 8 ) and D ( −1, 6 ) can be joined to form a parallelogram.


9. A triangle ABC has vertices A ( −2, −2 ) , B ( 1, 8 ) and C ( 6, 2 ) . If the points D and E are the midpoints of AB and AC , show that | ED | = 1


__ 2 | BC | .


10. Points A (−1, 0 ) , B ( 0, 3 ) , C ( 8, 11 ) and D (x, y) are points on the Cartesian plane. Find the coordinates of D if ABCD is a parallelogram.


9B Taking it FURTHER


1. The diagram shows the gable end of a house. The total height is 14 m. The height to roof level is 8 m, i.e. |AE| = 8 m. A is the point (2, 0). B is the point (18, 0).


y D E C 14 m x


(i) Write down the coordinates of the points C, D and E.


(ii) Find the slope of the rafter [ED].


(iii) Calculate the total length of wood needed to build the uprights AE and BC and the pitched piece for the roof EDC .


(iv) Find the area of the gable.


9 Working with the coordinate plane


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