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Superimposition of Shapes

2 questions

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Question 1Question →

Which composite figure correctly corresponds to each set of geometric components? Match each set of transparent geometric components (Sets 1-3) to its correct superimposed composite figure (Figures X-Z). Assume the base square remains stationary while the overlay square undergoes the indicated rotation before being placed exactly on top of the base square.

Click a left item, then click its matching right item

Items

Set 1: Base square with a diagonal line from top-left to bottom-right. Overlay square has a solid circle in the top-left quadrant, rotated 90° clockwise.
Set 2: Base square with a diagonal line from bottom-left to top-right. Overlay square has a solid circle in the top-left quadrant, rotated 180°.
Set 3: Base square with a diagonal line from bottom-left to top-right. Overlay square has a solid circle in the bottom-left quadrant, rotated 90° clockwise.

Matches

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Answer

Set 1 matches Figure X, Set 2 matches Figure Z, and Set 3 matches Figure Y.
Each correct pairing strictly follows spatial transformation rules. By systematically tracking the starting quadrant of the circle in the overlay, applying the stated degree and direction of rotation, and laying it over the specified diagonal base, the correct composite image can be logically deduced.

Step-by-Step Solution

1
Analyze Set 1 rotation and layering.
The top-left circle moves to the top-right. Placed over a top-left to bottom-right diagonal, this matches Figure X.
A 90-degree clockwise rotation shifts elements to the next adjacent quadrant in a clockwise direction.
2
Analyze Set 2 rotation and layering.
The top-left circle moves to the bottom-right. Placed over a bottom-left to top-right diagonal, this matches Figure Z.
A 180-degree rotation shifts elements diagonally to the completely opposite quadrant.
3
Analyze Set 3 rotation and layering.
The bottom-left circle moves to the top-left. Placed over a bottom-left to top-right diagonal, this matches Figure Y.
A 90-degree clockwise rotation shifts the bottom-left quadrant directly up to the top-left quadrant.

Key Concept

Superimposition of Shapes
Question 2Question →

A graphic artist is constructing a composite logo by stacking four clear square acetate slides perfectly on top of each other. Each slide features exactly one opaque geometric element. By observing how the shapes overlap in the final logo, determine the correct order in which the slides were stacked.

The final composite logo reveals the following depth cues:
- A thick light gray diagonal line spans the graphic, but its central portion is completely blocked from view by a large black circle.
- A medium white square sits perfectly centered inside the black circle, fully visible against the black background.
- A thin dark gray horizontal line stretches straight across the logo, passing visibly over the white square, the black circle, and the exposed ends of the diagonal line without interruption.

Arrange the four acetate slides in their correct stacking sequence from the BOTTOM layer (placed first) to the TOP layer (placed last).

Drag items to arrange them in the correct order

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Answer

The correct stacking order from bottom to top is: the slide with the light gray diagonal line, followed by the slide with the black circle, then the slide with the white square, and finally the slide with the dark gray horizontal line on top.
In superimposition problems involving opaque shapes, visual occlusion determines the stacking sequence. A shape that is partially hidden by another must be positioned underneath it. The diagonal line is hidden by the circle, placing it at the bottom. The circle is partially obscured by the square, placing it second. The square is overlaid by the horizontal line, placing it third. The horizontal line is completely uninterrupted, making it the top layer.

Step-by-Step Solution

1
Identify the bottommost layer by finding the shape that is hidden by others.
The thick light gray diagonal line is hidden by the large black circle, meaning it must be beneath it.
An opaque element covering another indicates it is layered on top, leaving the obscured element underneath.
2
Determine the relative position of the black circle and the white square.
The white square is fully visible against the black circle, meaning the square is placed above the circle.
If the circle were above the square, the square would be completely hidden by the opaque black circle.
3
Identify the topmost layer that covers all other elements.
The thin dark gray horizontal line crosses over the square, circle, and diagonal line without interruption.
A continuous, unbroken line passing over all other shapes must be the final layer placed on top.

Key Concept

Visual occlusion and depth order in superimposed geometric layers
Superimposition of Shapes Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) | Examkin