Select the option that is related to the third figure in the same way as the second figure is related to the first figure. Follow the analogy- Figure 1 : Figure 2 :: Figure 3 : ?

Correct — C. The figure is turned upside down, contents included.

Rule: reflect the whole figure in a horizontal axis — whatever was at the top ends up at the bottom.

fig(i) is a five-sided house outline: a flat base, two vertical sides, a peak at the top. fig(ii) is that outline inverted — flat across the top, vertical sides, and the point now at the bottom.

fig(iii) is the same house outline with a small upright triangle drawn inside it.

Inverting it gives a flat top, a point at the bottom, and the inner triangle now pointing down. That is option (c).

Why the others are wrong

• (a)
  Option (a) inverts the outline correctly but the inner triangle has disappeared. Nothing in the step from fig(i) to fig(ii) removes content from the figure.
• (b)
  Option (b) keeps the outline as a house with its peak at the top and turns only the small triangle. The operation acts on the whole figure, outline included.
• (d)
  Option (d) is fig(iii) redrawn unchanged — peak up, inner triangle up. No transformation has been applied at all.

A figure analogy asks you to name one operation that carries figure 1 to figure 2, then apply it to figure 3 without improvising.

The operation is nearly always one of a short list: rotate by a stated angle, reflect in a vertical or horizontal axis, add or delete an element, or shade something.

Here the outline is symmetric about its vertical axis, so a 180-degree rotation and a horizontal-axis reflection produce the same picture. Either description will do.

What decides the item is that the inner element turns with the outline rather than independently of it.

Key facts

• fig(i) and fig(iii) share the same five-sided outline: flat base, two vertical sides, a peak on top.
• fig(ii) is fig(i) reflected in a horizontal axis, which moves the peak to the bottom.
• A shape symmetric about its vertical axis looks identical after a 180-degree rotation and after a horizontal-axis reflection.

Common traps

• Turning the inner element but leaving the outline as it was.
• Dropping the inner element because an empty outline looks like a cleaner answer.
• Calling the step a rotation and then rotating by 90 degrees instead of 180.

No directly related past PYQ was found.