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:
Height of shadow=23 of height of screen=23×1.5 m=1.0 mHeight of puppetHeight of shadow=0.20.2+0.6Height of puppet1=0.20.8Height of puppet=0.25 m=25 cm




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)
Scale factor=2+62   =82   =4

(b)
Height of pillarHeight of shadow=14Height of pillar1.2=14Height of pillar=14×1.2 m=0.3 m




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:
Height of candleHeight of shadow=3030+9015 cmHeight of shadow=14Height of shadow=15 cm×4=60 cm34 of height of screen=60 cmHeight of screen=43×60 cm  =80 cm


10.2.1 Transformations II, PT3 Focus Practice


10.2.1 Transformations II, PT3 Focus Practice

Question 1:
In the diagram, ∆P’Q’R’ is the image of ∆PQR under an enlargement.

 
(a) State the scale factor of the enlargement.
(b)   If the area of ∆PQR = 7 cm2, calculate the area of ∆P’Q’R’.

Solution:
(a)
Scale factor, k=P'Q'PQ=63=2

(b)
Area of image = k× Area of object
Area of ∆P’Q’R’ = 22 × 7
 = 28 cm2


Question 2:
In diagram below, OP’Q’ is the image of OPQ under an enlargement with centre O.


Given PQ = 4cm, calculate the length, in cm, of P’Q’.

Solution:
P'Q'PQ=OP'OPP'Q'4=93P'Q'=93×4=12 cm



Question 3:
In diagram below, PQ’R’S’ is the image of PQRS under an enlargement.
 
Calculate the length, in cm, of SS’.

Solution:
PSPS'=PQPQ'PS36=416PS=416×36 =9 cmSS'=369 =27 cm



Question 4:
On the Cartesian plane, Q’R’S’ is the image of ∆ QRS under an enlargement of centre T.
 
State the coordinates of T.

Solution:

 
Coordinates of T = (4, 4).


Question 5:
In diagram below, quadrilateral AFGH is the image of ABCD under an enlargement.



(a) Find the scale factor of the enlargement.
(b) The area represented by the quadrilateral AFGH is 15cm2. Find the area, in cm2, represented by the shaded region.

Solution:
(a)
Scale factor=36+3=39=13

(b)
Area of image = k× Area of object
15=(13)2×Area of objectArea of object=15×9=135Area of shaded region=13515   =120cm2
 

10.1 Transformations II


10.1 Transformations II
 
10.1.1 Similarity
Two shapes are similar if
  (a) the corresponding angles are equal and
  (b)   the corresponding sides are proportional.

Example:
Quadrilateral ABCD is similar to quadrilateral JKLM because

A=J=90oB=K=50oC=L=130oD=M=90o

(All the corresponding angles are equal.)

ABJK=510=12BCKL=48=12CDLM=2.55=12ADJM=36=12

(All the corresponding sides are proportional.)


10.1.2 Enlargement
1. Enlargement is a type of transformation where all the points of an object move from a fixed point at a constant ratio.
 
2. The fixed point is known as the centre of enlargement and the constant ratio is known as the scale factor.
Scale factor=length of side of imagelength of side of object

3. 
The object and the image are similar.
 
4. If A’ is the image of A under an enlargement with centre O and scale factor k, then OA'OA=k
  • if k > 0, then the image is on the same side of the object.
  • if k < 0, then the image is on the opposite side of the object.
  • if –1 < k < 1, then the size of the image is a reduction of the size of the object.
5. Area of image = k2 × area of object.

9.2.2 Scale Drawings, PT3 Focus Practice


Question 6:
Diagram below shows an irregular pentagon.


By using the scale 1 : 200, complete the scale drawing in the answer space provided. The grid has equal square with sides of 1 cm.

Answer:


Solution:






Question 7:
Diagram below shows polygon.


(a) If the polygon is redrawn using the scale 1 : 500, calculate the length of side drawn for the side 15 m.
(b) On the square grids in the answer space, redraw the polygon using the scale 1 : 500. The grid has equal squares with sides of 1 cm.

Answer:
(a)Length of side of the drawing=155=3 cm

(b)


9.2.1 Scale Drawings, PT3 Focus Practice


Question 1:
Diagram below shows polygon P drawn on a grid of equal squares with sides of 1 unit.

On the grid in the answer space, redraw polygon P using the scale 1 : 12.
The grid has equal squares with sides of 1 unit.

Answer:




Question 2:
Diagram below shows polygon W drawn on a grid of equal squares with sides of 1 unit.

On the grid in the answer space, redraw polygon W using the scale 1 : 2.
The grid has equal squares with sides of 1 unit.

Answer:



Question 3:
Diagram below shows a polygon PQRSTU.



(a) If the polygon is redrawn using the scale 1 : 400, calculate the length of PQ.
(b) In the answer space, redraw the polygon using the scale 1 : 400. The grid has equal squares with sides of 1 cm.

Answer:
(a)

Length of PQ=4800 cm400 =12 cm

(b)




Question 4:
Diagram below shows a polygon.



On the grid in the answer space, redraw the polygon using the scale 1 : 500. The grid has equal squares with sides of 1 cm.

Answer:

Actual length Drawing
45 m = 4500 cm 4500 ÷ 500 = 9 cm
20 m = 2000 cm 2000 ÷ 500 = 4 cm
35 m = 3500 cm 3500 ÷ 500 = 7 cm
10 m = 1000 cm 1000 ÷ 500 = 2 cm





Question 5:
Diagram below shows a polygon.


(a) If the polygon is redrawn using the scale 1 : 300, calculate the length, in cm, the drawing for the side 24 m.
(b) In the answer space, redraw the polygon using the scale 1 : 300. The grid has equal squares with sides of 1 cm.

Answer:
(a)
Length of side of the drawing=2400 cm300=8 cm

(b)