Unit 5
4 marks · EasyA triangle is reflected in the y-axis and then translated by the vector (4, -1) on a grid. One vertex of the triangle is at (2, 3). A table shows the number of students in four classes who completed a geometry exercise: 12, 15, 13, 20.
Write down the coordinates of the vertex after reflection in the y-axis.
Write the new coordinates after the translation.
Calculate the mean number of students who completed the exercise.
If one more student completes the exercise in the first class, how does the mean change? Work out the new mean.
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.
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(a) (-2, 3)
(b) (2, 2)
(c) 15
(d) 15.25
Common mistakes: Using wrong sign for y-axis reflection; Adding translation vector incorrectly; Mean not recalculated after adding new value
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correct reflection coordinate: (−2, 3)
A1 (b) · 1 mark · Correct translation to (2, 2)
M1 (c) · 1 mark · Method to calculate mean, answer: 15
A1 (d) · 1 mark · Correct new mean: 15.25
Worked solution
(a) Reflection in the y-axis: change sign of x; (2, 3) → (−2, 3).
(b) Translate by (4, −1): (−2, 3) → (−2 + 4, 3 − 1) = (2, 2).
(c) Mean = (12 + 15 + 13 + 20) / 4 = 60 / 4 = 15
(d) New total is 61, so mean = 61 / 4 = 15.25