Date | May 2021 | Marks available | 2 | Reference code | 21M.1.SL.TZ2.2 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Find | Question number | 2 | Adapted from | N/A |
Question
An inclined railway travels along a straight track on a steep hill, as shown in the diagram.
The locations of the stations on the railway can be described by coordinates in reference to x, y, and z-axes, where the x and y axes are in the horizontal plane and the z-axis is vertical.
The ground level station A has coordinates (140, 15, 0) and station B, located near the top of the hill, has coordinates (20, 5, 250). All coordinates are given in metres.
Station M is to be built halfway between stations A and B.
Find the distance between stations A and B.
Find the coordinates of station M.
Write down the height of station M, in metres, above the ground.
Markscheme
attempt at substitution into 3D distance formula (M1)
AB=√(140-20)2+(15-5)2+2502 (=77
A1
[2 marks]
attempt at substitution in the midpoint formula (M1)
A1
[2 marks]
A1
[1 mark]