1.12: Past-paper question 8

4PM1/1R/June/2024 — Question 8 · 10 marks

1.12 diagram 1
Figure 3 shows a trapezium ABCD\displaystyle ABCD
BC→=3aAD→=5aCD→=2b\overrightarrow{BC}=3\mathbf{a} \quad \overrightarrow{AD}=5\mathbf{a} \quad \overrightarrow{CD}=2\mathbf{b}
(a) Find AB→\displaystyle \overrightarrow{AB} as a simplified expression in terms of a\displaystyle \mathbf{a} and b\displaystyle \mathbf{b}
(1)
The diagonals BD\displaystyle BD and AC\displaystyle AC intersect at point X\displaystyle X where BX→=kBD→\displaystyle \overrightarrow{BX}=k\overrightarrow{BD}
(b) Using a vector method, find the value of k\displaystyle k
(5)
(c) Find the ratio of the area of triangle CXD\displaystyle CXD : area of the trapezium ABCD\displaystyle ABCD
(4)