Analogy Completion With a Chiral Turn
On an analogy item you have 35 seconds. Figure A is a square with a dot at the top-left corner and a short line attached to the middle of the right side, pointing right. Figure B is the same square with the dot at the top-right corner and the short line attached to the middle of the bottom side, pointing down. Figure C is a regular pentagon with a dot at the top vertex and a short line attached to the middle of the right side, pointing right. You must choose the figure that completes 'A is to B as C is to ?'. The options are: 1) pentagon with dot at the rightmost vertex and line on the bottom side pointing down; 2) pentagon with dot at the rightmost vertex and line on the right side pointing right; 3) pentagon with dot at the leftmost vertex and line on the bottom side pointing down; 4) pentagon with dot at the top vertex and line on the right side pointing right. You notice options 1 and 3 both move the dot away from the top.
1. State the transformation in A to B and apply it to C. Which option follows?
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A to B is a 90° clockwise rotation of the whole figure about its centre. Check the two landmarks: the dot moves from top-left to top-right; the right-side line moves to the bottom side and points down. A reflection would not produce both: a vertical reflection would put the line on the left, and a diagonal reflection would put it on the top or bottom in a different relation to the dot. Apply the same 90° clockwise rotation to C: the top-vertex dot moves to the rightmost vertex; the right-side line moves to the bottom side and points down. Option 1 matches. Option 2 rotates the dot but leaves the line; option 3 is a mirror image; option 4 is unchanged.
2. How would you separate your chosen option from option 3 with one landmark check?
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Use a signed angle from the dot to the line around the centre. In C, going clockwise from the dot to the line is 90°. A rotation preserves that signed angle; a reflection reverses it. In option 1, the dot is at the rightmost vertex and the line is at the bottom side; going clockwise from the dot to the line is still 90°. In option 3, the dot is at the leftmost vertex and the line is at the bottom; going clockwise from the dot to the line is 270°, so the sign is reversed. Option 3 therefore cannot be obtained by rotation alone and is eliminated.