SPM Practice (Long Questions)

Question 9 (12 marks):
(a) Diagram 7.1 shows K (5, 1) drawn on a Cartesian plane.
Diagram  7.1

Transformation T is a translation $\left(\begin{array}{l}-3\\ 4\end{array}\right)$
Transformation P is a reflection in the line y = 2.
State the coordinates of the images of point K under each of the following transformations:
(i) T²,
(ii) TP.


(b) Diagram 7.2 shows two pentagons KLMNP and QRSTU, drawn on a Cartesian plane.

Diagram  7.2

(i) Pentagon QRSTU  is the image of pentagon KLMNP under the combined transformation WV.
Describe in full the transformation:
(a) V,
(b) W.

(ii) It is given that pentagon QRSTU represents a region with an area of 90 m².
Calculate the area, in m², of pentagon KLMNP.


Solution:
(a)



(i) TT = K(5, 1) → T₁ → K’(2, 5) ) → T₂ → K’’(–1, 9)
(ii) TP =  K(5, 1) → P → K’(5, 3) → T → K’’(2, 7)


(b)


(b)(i)(a)
V: 90^o rotation in clockwise direction at point K(3, 7).

(b)(i)(b)
W: Enlargement at point (1, 6) with scale factor 3.

(b)(ii)
Area of QRSTU = (scale factor)² × area of object
Area of QRSTU = 3² × Area of KLMNP
90 m² = 9 × Area of KLMNP
Area of KLMNP = 90/9 = 10 m²