10.2.2 Transformations II, PT3 Focus Practice

Question 6:
Diagram below shows a ‘Wayang Kulit’ performed by Tok Dalang. The height of the screen use is 1.5 m. The shadow on the screen is ⅔ the height of the screen.
What is the height, in cm, of the puppet used by Tok Dalang?

Solution:
$\begin{array}{l}\text{Height of shadow}\\ =\frac{2}{3}\text{ of height of screen}\\ =\frac{2}{3}\times 1.5\text{ m}\\ =1.0\text{ m}\\ \\ \frac{\text{Height of puppet}}{\text{Height of shadow}}=\frac{0.2}{0.2+0.6}\\ \\ \frac{\text{Height of puppet}}{\text{1}}=\frac{0.2}{0.8}\\ \\ \text{Height of puppet}\\ =0.25\text{ m}\\ =25\text{ cm}\end{array}$

Question 7:
Diagram below shows the shadow of a pillar form on the wall from the light of a spotlight. 
(a) State the scale factor of the enlargement.
(b) Find the height of the pillar. 

Solution:
(a)
$\begin{array}{l}\text{Scale factor}=\frac{2+6}{2}\\ =\frac{8}{2}\\ =4\end{array}$

(b)
$\begin{array}{l}\frac{\text{Height of pillar}}{\text{Height of shadow}}=\frac{1}{4}\\ \\ \frac{\text{Height of pillar}}{1.2}=\frac{1}{4}\\ \\ \text{Height of pillar}=\frac{1}{4}\times 1.2\text{ m}\\ =0.3\text{ m}\end{array}$

Question 8:
In diagram below, a torch light is used to form a shadow of a candle on the screen.


The height of the candle is 15 cm.
If the height of the shadow of the candle is ¾ of the height of the screen, find the height of the screen.

Solution:
$\begin{array}{l}\frac{\text{Height of candle}}{\text{Height of shadow}}=\frac{30}{30+90}\\ \\ \frac{15\text{ cm}}{\text{Height of shadow}}=\frac{1}{4}\\ \\ \text{Height of shadow}=15\text{ cm}\times 4\\ =60\text{ cm}\\ \\ \frac{3}{4}\text{ of height of screen}=60\text{ cm}\\ \text{Height of screen}=\frac{4}{3}\times 60\text{ cm}\\ =80\text{ cm}\end{array}$