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I feel like an idiot for asking, I got this question in a practice paper, it's the first question so it's easy. enter image description here

The question is "describe fully the single transformation that will map shape P onto shape Q"

To me this is simply "Rotation 180 degrees about the point (0,1)" However the mark scheme thinks it is 90 degrees clockwise?

Is there any way this could be true, it's not the first mistake in the markscheme, but I need to be sure for my exam. (sorry if this question is to basic for here)

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The acute (45 degree) angle in shape P is "pointing" to the right, and the corresponding angle in shape Q is pointing down, so it looks like the angle of rotation must be 90 degrees clockwise. Another clue: if you rotate 180 degree about the point (0,1) then that pointy corner of shape P at (4,2) would move to (-4,0), and there's nothing there. –  Jyrki Lahtonen Jun 4 '11 at 10:22
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2 Answers

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I assume that by "transformation" they mean "isometry" (else there would be infinitely many different transformations mapping these shapes onto each other).

The mark scheme is right; this is a rotation through $90^\circ$ clockwise, but about the point $(-2,3)$, not $(0,1)$. My grasp of what may have made you think it's $180^\circ$ is probably insufficient for me to say anything helpful about that, but in case you were focussing on the points at $(1,2)$ and $(-1,0)$, which are indeed related by a rotation through $180^\circ$ about $(0,1)$, note a) that these don't correspond to each other in the shapes and b) that no other pairs of points are related by this rotation.

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Thanks, I feel quite stupid now :) After seeing this I can't for the life of me understand how I thought it was 180 degrees :). –  Jonathan. Jun 4 '11 at 10:58
    
@Jonathan: No need to feel stupid -- live and learn :-) –  joriki Jun 4 '11 at 11:20
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Your mark scheme seems to be correct. Look at the small line segment (1,4)-(2,4) in the polygon. It maps to the vertical segment (-1,0)-(-1,1).

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Ok I see it is 90 degrees clockwise but it's not about the point (0,1). –  Jonathan. Jun 4 '11 at 10:58
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