SPM 2021 Add Maths Trial Paper (Selangor) – Paper 1 (Question 7)

Question 7:
Solutions by scale drawing is not accepted.

Diagram 2

Diagram 2 shows a trapezium ABCDE where BC is the height of the trapezium ABCDE.
Find
(a) the value of k, (2 marks)
(b) the coordinates of point C. (4 marks)


Solution:
(a)

$\begin{array}{l}{m}_{AB}=m_{ED}\\ \frac{4-3}{7-4}=\frac{0-\left(-1\right)}{k-0}\\ \frac{1}{3}=\frac{1}{k}\\ k=3\end{array}$


(b)

$\begin{array}{l}\text{Equation }EC,\text{ point }E(2,-1),\\ y-\left(-1\right)=\frac{1}{3}\left(x-2\right)\\ y+1=\frac{1}{3}\left(x-2\right)\\ 3y+3=x-2\\ x=3y+5\mathrm{\dots ..}(1)\\ \\ m_{ED}\times m_{BC}=-1\\ \frac{1}{3}\times m_{BC}=-1\\ m_{BC}=-3\\ \\ \text{Equation }BC,\text{ point }E(7,4),\\ y-4=-3\left(x-7\right)\\ y-4=-3x+21\\ y=-3x+25\mathrm{\dots ..}(2)\\ \\ Substitute(1)into(2),\\ y=-3\left(3y+5\right)+25\\ y=-9y-15+25\\ 10y=10\\ y=1\\ \\ \text{From (1),}\\ x=3\left(1\right)+5\\ x=8\\ \therefore \text{Point }C=\left(8,1\right).\end{array}$