2019 Nov P2 Q3

Question 3

In the diagram, $P$ , $R(3\,;\,5)$ , $S(-3\,;\,-7)$ and $T(-5\,;\,k)$ are vertices of a trapezium $PRST$ and $PT \parallel RS$ . $RS$ and $PR$ cut the $y$ -axis at $D$ and $C(0\,;\,5)$ respectively. $PT$ and $RS$ cut the $x$ -axis at $E$ and $F$ respectively. $P\hat EF=\theta$ .

$3.1$	Write down the equation of $PR$ .	$(1)$
$3.2$	Calculate the:
$\quad 3.2.1$	Gradient of $RS$	$(2)$
$\quad 3.2.2$	Size of $\theta$	$(3)$
$\quad 3.2.3$	Coordinates of $D$	$(3)$
$3.3$	If it is given that $TS=2\sqrt{5}$ , calculate the value of $k$ .	$(4)$
$3.4$	Parallelogram $TDNS$ , with $N$ in the $4^{th}$ quadrant, is drawn. Calculate the coordinates of $N$ .	$(3)$
$3.5$	$\Delta PRD$ is reflected about the $y$ -axis to form $\Delta P^\prime R^\prime D^\prime$ . Calculate the size of $R\hat DR^\prime$ .	$(3)$
		$\textbf{[19]}$