Unit 5
4 marks · Normal6. A parallelogram has vertices at A(1,1), B(5,1), C(7,4), D(3,4).
It is mapped onto another parallelogram by an enlargement of scale factor 2, centre (1,1).
A tree diagram is used to calculate the probability of randomly selecting two red marbles from a bag containing 2 red and 3 blue marbles, without replacement.
Write down the coordinates of the image of C after the enlargement.
Describe fully the transformation that maps the original parallelogram onto its image.
Calculate the probability that both marbles chosen are red.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) (13, 7)
(b) Enlargement, scale factor 2, centre (1,1)
(c) 1/10
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States correct coordinates after enlargement
B2 (b) · 1 mark · Fully describes transformation
M1 (c) · 1 mark · Sets up correct probability fractions
A1 (c) · 1 mark · Gives answer 1/10 in simplest form
Worked solution
a) (7,4) under enlargement from (1,1): (7-1)×2 +1 = 13, (4-1)×2 +1 = 7.
b) Enlargement, scale factor 2, centre (1,1).