# 10.2 Transformations II, PT3 Focus Practice

10.2 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)
$\text{Scale factor,}k=\frac{P\text{'}Q\text{'}}{PQ}=\frac{6}{3}=2$

(b)
Area of image = k2× Area of object
Area of ∆P’Q’R’ = 22 × 7
= 28 cm2

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

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

Solution:
$\begin{array}{l}\frac{P\text{'}Q\text{'}}{PQ}=\frac{OP\text{'}}{OP}\\ \frac{P\text{'}Q\text{'}}{4}=\frac{9}{3}\\ P\text{'}Q\text{'}=\frac{9}{3}×4\\ \text{}=12\text{cm}\end{array}$

Question 3:
In diagram below, PQ’R’S’ is the image of PQRSunder an enlargement.

Calculate the length, in cm, of SS’.

Solution:
$\begin{array}{l}\frac{PS}{PS\text{'}}=\frac{PQ}{PQ\text{'}}\\ \frac{PS}{36}=\frac{4}{16}\\ PS=\frac{4}{16}×36\\ \text{}=9\text{cm}\\ SS\text{'}=36-9\\ \text{}=27\text{cm}\end{array}$

Question 4:
On the Cartesian plane, Q’R’S’ is the image of ∆ QRSunder 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 ABCDunder an enlargement.

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

Solution:
(a)
$\begin{array}{l}\text{Scale factor}\\ =\frac{3}{6+3}=\frac{3}{9}=\frac{1}{3}\end{array}$

(b)
Area of image = k2× Area of object
$\begin{array}{l}15={\left(\frac{1}{3}\right)}^{2}×\text{Area of object}\\ \text{Area of object}=15×9=135\\ \\ \text{Area of shaded region}=135-15\\ \text{}=120c{m}^{2}\end{array}$