Question

lA 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 above, , PR
is 25.4 cm and RT is 50.8 cm. The length of the cat RQ, in the original print
is 6.1 cm. What is the length of TS in the enlargement.​

Answer 1

Given :   PR is 25.4 cm and RT is 50.8 cm. The length of the  cat RQ, in the  original print is 6.1 cm .

The ratio of  PR to PT is always equal to the ratio of PQ to PS

To Find : What is the length of TS in the enlargement.

(i) 18.3 cm (ii) 12.2 cm (iii) 6.1 cm (iv) 11 cm

Solution:

PR/ PT   = PQ /  PS   given

∠P  = ∠ P   Common  

Using SAS similarity

ΔPRQ ≈ ΔPTS  

=> PR/PT = PQ/PS = RQ/TS

PR= 25.4

RT = 50.8

PT = PR + RT =  25.4 +  50.8  = 76.2

RQ = 6.1

=> 25.4  / 76.2  = 6.1 /TS

=> 1/3 = 6.1/TS

=> TS = 3 x 6.1

=> TS = 18.3 cm

length of TS in the enlargement.​ = 18.3 cm

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