Unit 9
8 marks · EasyThe graph of for is sketched below.
Write down the equation of the graph reflected in the x-axis.
A right-angled triangle has sides AB = 4 cm, BC = 3 cm and the right angle is at B. The triangle is a face on a cuboid.
Calculate the length AC.
The cuboid from part b has a height BD = 8 cm, perpendicular to triangle ABC. Find the length from A to D.
Describe how the transformation in part a and the 3D length calculation in part c both involve symmetry or distance.
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) y = -f(x) · must show Correct transformation equation
(b) AC = 5 cm · must show Correct use of Pythagoras' theorem
(c) AD = sqrt(4^2+8^2) = sqrt(80) = 8.9 cm · must show Correct 3D diagonal using Pythagoras
(d) Both involve measuring changes: the reflection creates symmetry across an axis, while 3D Pythagoras measures direct spatial distance; both use geometric reasoning. · must show Relevant connection explained
Show mark scheme and worked solution
Marking points
B1 (a) · 2 marks · States correct transformed equation.
M1 (b) · 1 mark · Uses Pythagoras with correct sides.
A1 (b) · 1 mark · AC = 5 cm to 1 d.p.
M2 (c) · 1 mark · Uses 3D Pythagoras on AB and BD.
A2 (c) · 1 mark · AD = 8.9 cm to 1 d.p.
B2 (d) · 2 marks · Describes link between symmetry (transformation) and geometric distance.
Worked solution
a) The reflection in the x-axis is y = -f(x).
b) AC = sqrt(AB^2 + BC^2) = sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5 cm
c) AD = sqrt(AB^2 + BD^2) = sqrt(4^2 + 8^2) = sqrt(16 + 64) = sqrt(80) = 8.9 cm
d) Both the transformation and the 3D length calculation use properties of geometry. The reflection creates a mirror image (symmetry), and finding a diagonal in 3D measures the shortest direct distance—both are about changes or symmetry in geometric space.