Question

For the Transformation T, write the T^-1.

Answer 1

The 3rd selection is appropriate.

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(1/5)(5x) = x, so the inverse transformation returns the original. Not so for the other choices.

Answer 2

Answer:  The correct option is

(C) $T^{-1}(x,y)\rightarrow \left(\dfrac{1}{5}x,\dfrac{1}{5}y\right).$

Step-by-step explanation:  We are given a transformation T defined as :

$T:(x,y)\rightarrow (5x,5y).$

We are to find the inverse transformation $T^{-1}(x,y).$

From the given transformation, we have

$T:(x,y)\rightarrow (5x,5y)\\\\\Rightarrow T^{-1}(5x,5y)=(x,y).$

Let us consider that

$5x=z~~~~~~\Rightarrow x=\dfrac{z}{5},\\\\\\5y=t~~~~~~\Rightarrow y=\dfrac{t}{5}.$

Therefore, we get

$T^{-1}(5x,5y)\rightarrow(x,y)\\\\\Rightarrow T^{-1}(z,t)\rightarrow \left(\dfrac{z}{5},\dfrac{t}{5}\right)\\\\\\\Rightarrow T^{-1}(x,y)\rightarrow \left(\dfrac{1}{5}x,\dfrac{1}{5}y\right).$

Thus, (C) is the correct option.