Date | November 2019 | Marks available | 2 | Reference code | 19N.2.SL.TZ0.S_2 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Write down | Question number | S_2 | Adapted from | N/A |
Question
Consider the lines L1L1 and L2L2 with respective equations
L1:y=−23x+9L1:y=−23x+9 and L2:y=25x−195L2:y=25x−195.
A third line, L3L3, has gradient −34−34.
Find the point of intersection of L1L1 and L2L2.
Write down a direction vector for L3L3.
L3L3 passes through the intersection of L1L1 and L2L2.
Write down a vector equation for L3L3.
Markscheme
valid approach (M1)
eg L1=L2L1=L2, x=12x=12, y=1y=1
(12, 1)(12, 1) (exact) A1 N2
[2 marks]
(−43)(−43) (or any multiple of (−43)(−43)) A1 N1
[1 mark]
any correct equation in the form r = a + ttb (accept any parameter for tt) where
a is a position vector for a point on L1L1, and b is a scalar multiple of (−43)(−43) A2 N2
eg r =(121)+t(−43)=(121)+t(−43)
Note: Award A1 for the form a + tb, A1 for the form L = a + tb, A0 for the form r = b + ta.
[2 marks]