Reflection and Congruence

Reflection and Congruence

  1. Given that A’ (3, -3) is the image of A (-1, -5) under a reflection. Find the equation of the mirror line in the form of

 ax + by + c = 0       (4 mks)

  1. Three planes A, B and C leave an airport P simultaneously at 9.30a.m. Plane A flies on

a bearing of 070o from P at a speed of 400km/h. Plane B flies on a bearing of 290oat a

speed of 500km/h. Plane C flies on a bearing of 162o from P at a speed of 300km/h.

(Use scale drawing for this question)

(a) Show by scale drawing, the relative positions of the 3planes A, B and C three hours

after leaving  airport P. (Use scale 1cm represents 200km)

(b) After 3 hours, B turns and head straight to the current position of A at the same

speed it had.   Determine the scale drawing, the time it takes to reach this point, to

the nearest minute

(c) Determine the bearing and distance of B from C after the first 3 hours of flight after

leaving P                                                                                                                           

  1. Triangle PQR has vertices P(3,2), Q(-1,1) and R(-3,-1).

(a) Draw PQR on the grid provided.                                                                                      (1mk)

(b) Under a rotation the vertices of P1Q1R1 are P1(1,4), Q1(2,0) and R1(4,-1). Find the centre and angle of rotation using points P and Q.                                                                                (4mks)

(c) Triangle PQR is enlarged with scale factor 3 centre O(0,0) to give triangle P2Q2R2. Draw triangle P2Q2R2 and state its co-ordinates.                                                                              (2mks)

(d) Triangle P1Q1R1 undergoes reflection in line y = -x to give triangle P3Q3R3. draw P3Q3R3 and state its coordinates.                                                                                                                        (3mks)

  1. The figure below shows part of a diagram of rotation symmetry order 3 about a point O. Complete the diagram.                                                                                                                            (3mks)

  1. In the figure below, triangle AIBICI is the image of triangle ABC under a rotation, centre O.

By construction, find and label the centre O of the rotation.

Hence, determine the angle of the rotation.    \


  1. The ratio of the lengths of the corresponding sides of two similar rectangular water

tanks are 3: 5. The volume of the smaller tank is 8.1m3. Calculate the volume of the

larger tank

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