Transformations - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Transformations.

Flagged Up

KS 3 Short Challenge Level:

Weekly Problem 31 - 2008
The flag is given a half turn anticlockwise about the point O and is then reflected in the dotted line. What is the final position of the flag?

Peri the Winkle

KS 3 Short Challenge Level:

Weekly Problem 31 - 2014
Peri the winkle starts at the origin and slithers around some semicircles. Where does she end her expedition?

Potatoes

KS 3 Short Challenge Level:

Weekly Problem 19 - 2009
When I looked at the greengrocer's window I saw a sign. When I went in and looked from the other side, what did I see?

Reflected Back

KS 3 Short Challenge Level:

Weekly Problem 18 - 2015
Beatrix relfects the letter P in all three sides of a triangle in turn. What is the final result?

Semaphore

KS 3 Short Challenge Level:

Weekly Problem 34 - 2009
I am standing behind five pupils who are signalling a five-digit number to someone on the opposite side of the playground. What number is actually being signalled?

Back in Time

KS 3 Short Challenge Level:

Weekly Problem 29 - 2015
How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

Grid Without Lines

KS 3 Short Challenge Level:

Weekly Problem 40 - 2010
Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?

Sharks Are Symmetric

KS 3 Short Challenge Level:

Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?

Doubly Symmetric

KS 3 Short Challenge Level:

Weekly Problem 24 - 2016
What is the smallest number of additional lines that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?

Angular Reflection

KS 3 Short Challenge Level:

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?

KS 3 Short Challenge Level:

Weekly Problem 24 - 2011
Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?

Turning N Over

KS 3 Short Challenge Level:

Weekly Problem 34 - 2013
A card with the letter N on it is rotated through two different axes. What does the card look like at the end?

Kangaroo Hops

KS 3 Short Challenge Level:

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

Pendants

KS 4 Short Challenge Level:

What proportion of each of these pendants will be made of gold?

KS 4 Short Challenge Level:

Weekly Problem 48 - 2012
The curve $y=x^2−6x+11$ is rotated through $180^\circ$ about the origin. What is the equation of the new curve?

Half Area

KS 4 Short Challenge Level:

The horizontal red line divides this equilateral triangle into two shapes of equal area. How long is the red line?

Growing Triangle

KS 4 Short Challenge Level:

If the base and height of a triangle are increased by different percentages, what happens to its area?