GATE Civil 2023 Set 2 | GA | Question: 5

Question

Consider a circle with its centre at the origin $(\mathrm{O})$, as shown. Two operations are allowed on the circle.

Operation $1:$ Scale independently along the $\mathrm{x}$ and $\mathrm{y}$ axes.
Operation $2:$ Rotation in any direction about the origin.

Which figure among the options can be achieved through a combination of these two operations on the given circle?

• A.

• B.

• C.

• D.

Answer 1

Ans- A)

Comments

Scale independently along the x and y axes.

Here, we can think that while scaling we can scale in +x and -x independently like we do when we crop pictures (we have 4 different directions and in more advanced tools, 8 directions) but here only 2 directions (x and y) are allowed so both +x and -x will get scaled up or down at the same time and both +y and -y will get scaled up or down at the same time.

Scale: shape of the object will remain symmetric with respect to the axis of transformation after transformation also. size can grow or shrink.

PS: if scaling as above mentioned was allowed then all options would have been correct.

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Totally agree.

#insightful #keepitup

Answer 2

Ans – A)