# IMAT 2012 Q78 \[Transformations\]

**URL:** <https://imat.entermedschool.com/t/imat-2012-q78-transformations/277>\
**Category:** Past Papers Solutions Archives\
**Tags:** math, imat-2012\
**Created:** [May 8, 2022, 12:36am UTC](https://imat.entermedschool.com/t/imat-2012-q78-transformations/277 "2022-05-08T00:36:52Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![AhdOmer](https://imat.entermedschool.com/user_avatar/imat.entermedschool.com/ahdomer/32/275_2.png) [@AhdOmer](https://imat.entermedschool.com/u/AhdOmer)\
**Post date:** [May 8, 2022, 12:36am UTC](https://imat.entermedschool.com/t/imat-2012-q78-transformations/277/1 "2022-05-08T00:36:52Z")

</div>

ABCDE is a regular pentagon. The transformation R is a rotation about the origin and maps A to B, B to C, C to D, etc. The transformation S is a reflection in the y-­axis.

![image](https://imat.entermedschool.com/uploads/default/original/1X/2f0dced2db0c071a9ef051ae8e57976801eb410e.png)

Which of the following sequences of transformations (performed in the order that they are listed) would NOT leave vertex D in the same position?

A. R R S R S R  
B. S R  
C. S R R S R S  
D. R S R S  
E. R S R R

---

<div class="post-metadata">

**Author:** ![AhdOmer](https://imat.entermedschool.com/user_avatar/imat.entermedschool.com/ahdomer/32/275_2.png) [@AhdOmer](https://imat.entermedschool.com/u/AhdOmer)\
**Post date:** [May 20, 2022, 11:17am UTC](https://imat.entermedschool.com/t/imat-2012-q78-transformations/277/2 "2022-05-20T11:17:08Z")

</div>

The answer is **A** , sequence R R S R S R.

- By undergoing R twice, we are at back at A.

- By undergoing S, this leaves us still at A.

- By undergoing R once again, we are now at B.

- By undergoing S, we have completely left the pentagon and another R nor S can put us back on the pentagon respectively.

Therefore, A will not leave D at it’s start position.

---

<div class="post-metadata">

**Author:** ![Slawek\_Mincewicz](https://imat.entermedschool.com/user_avatar/imat.entermedschool.com/slawek_mincewicz/32/5858_2.png) [@Slawek\_Mincewicz](https://imat.entermedschool.com/u/Slawek_Mincewicz)\
**Post date:** [January 3, 2024, 11:05pm UTC](https://imat.entermedschool.com/t/imat-2012-q78-transformations/277/3 "2024-01-03T23:05:33Z")

</div>

I don’t think that the sequence “RR” brings us “back at A”; rather I think we’re with “A” at “C”. And now the vertical flip S makes what was “C” leave the original pentagon for good, a crime that could never be redressed :-). Hence, no further twisting and flipping will bring “D” to its original position and the answer is indeed (A).