Dilation stretches or shrinks a figure. The image created by a dilation is similar to the original figure. The scale factor (k) of dilation is the ratio of corresponding side lengths. The centre of dilation is a fixed point in the plane about which all points are expanded or contracted.
\(\frac{\text{image}}{\text{pre−image}}\) = \(\frac{A'C'}{AC}=\frac{C'B'}{CB}=\frac{A'B'}{AB}=\frac{2}{1}=k\) (Say).
Scale factor (k) :
• If k > 1, enlargement
• If 0 < k < 1, reduction
• If k = 1, congruence.
(i). From the above given information, triangles ABC and A′B′C′ are similar.
Which of the following options will hold good ?
(a) ∆BAC ~∆ A′B′C′
(b) ∆BCA ~∆ C′B′A′
(c) ∆CBA ~∆ B′C′A′
(d) ∆CAB ~∆ C′A′B′.
(ii). The dimensions of the model of a multi-storey building are 1.2 m × 75 cm × 2 m.
If the scale is 1 : 30, then what is the actual dimensions of the building ?
(a) 36 m × 22.5 m × 60 m
(b) 10.2 m × 2 m × 15 m
(c) 120 cm × 150 cm × 200 cm
(d) 24 m × 14.4 m × 80 m.
(iii). With what scale factor 0.9 m is to be multiplied to get the value of ‘h’ in the below given real life situation.
(a) 3 ∶ 1
(b) 1 ∶ 2
(c) 1 ∶ 3
(d) 2 ∶ 1.
(iv). A pantograph is a mechanical linkage connected in a manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a second pen. As we move the tracing pin of a pantograph along a figure, the pencil attached to the far end draws an enlargement. As the pantograph expands and contracts, the three brads and the tracing pin always form the vertices of a parallelogram. The ratio of PR to PT is always equal to the ratio of PQ to PS. Also, the suction cup, the tracing pin and the pencil remain collinear.
In the picture given below, PR is 25.4 cm and RT is 50.8 cm. The length of the star RQ, in the original point is 6.1 cm. What is the length of TS in the enlargement ?
(a) 18.3 cm
(b) 12.2 cm
(c) 6.1 cm
(d) 11 cm .
(v). In the picture given below, what is the height of PC if QC = 3 m where QC is 10 times of AB and DF is 4 times the width of a car where width of the car is 1.6 m.
(a) 33 m
(b) 64 m
(c) 44 m
(d) 11 m.
