Question 11:
(a) Diagram 8.1 shows two quadrilaterals, PQRS and TUVW.
Quadrilateral TUVW is the image of quadrilateral PQRS under a rotation.
State the corresponding side of QR and the corresponding angle of ∠TWV.
[2 marks]
Answer:
(a) Corresponding side: …………………………
corresponding angle: …………………………..
(b) Diagram 8.2 in the answer space shows two pentagons. Pentagon XWVUT is the image of pentagon PQRST under the combined transformation HG.
(i) It is given that transformation G is a reflection in the line PT. Draw the image of pentagon PQRST under the transformation G. [1 mark]
(ii) Hence, describe fully the transformation H. [3 marks]
(iii)(a) State the ratio of the area of pentagon PQRST to the area of pentagon XWVUT.
(b) The total area of pentagon PQRST and pentagon XWVUT is 240 cm2.
Calculate the area of pentagon PQRST.
[3 marks]
Answer:
Answer:
(a)
Corresponding side: UV or VU
Corresponding angle: ∠PSR or ∠RSP
(b)(i)
(b)(ii) Enlargement with scale factor 3 at centre T.
(b)(iii)(a) 1 : 9
(b)(iii)(b)
$$ \begin{aligned} &\text { The area of pentagon }\\ &\begin{aligned} P Q R S T & =\frac{240 \mathrm{~cm}^2}{(1+9)} \\ & =24 \mathrm{~cm}^2 \end{aligned} \end{aligned} $$
(a) Diagram 8.1 shows two quadrilaterals, PQRS and TUVW.
Quadrilateral TUVW is the image of quadrilateral PQRS under a rotation.
State the corresponding side of QR and the corresponding angle of ∠TWV.
[2 marks]
Answer:
(a) Corresponding side: …………………………
corresponding angle: …………………………..
(b) Diagram 8.2 in the answer space shows two pentagons. Pentagon XWVUT is the image of pentagon PQRST under the combined transformation HG.
(i) It is given that transformation G is a reflection in the line PT. Draw the image of pentagon PQRST under the transformation G. [1 mark]
(ii) Hence, describe fully the transformation H. [3 marks]
(iii)(a) State the ratio of the area of pentagon PQRST to the area of pentagon XWVUT.
(b) The total area of pentagon PQRST and pentagon XWVUT is 240 cm2.
Calculate the area of pentagon PQRST.
[3 marks]
Answer:
Answer:
(a)
Corresponding side: UV or VU
Corresponding angle: ∠PSR or ∠RSP
(b)(i)
(b)(ii) Enlargement with scale factor 3 at centre T.
(b)(iii)(a) 1 : 9
(b)(iii)(b)
$$ \begin{aligned} &\text { The area of pentagon }\\ &\begin{aligned} P Q R S T & =\frac{240 \mathrm{~cm}^2}{(1+9)} \\ & =24 \mathrm{~cm}^2 \end{aligned} \end{aligned} $$