Figure P shows the top view of a circular table top with few objects arranged on it for a sketching class. Numbers 1 to 24 in figure P represent different directions around the table from which students are sketching the objects. Which option gives the directions from which the sketches in Figure Q and R are drawn?
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In perspective problems, identify the object closest to the viewer in the sketch (the one that appears largest or lowest in the frame). Then, locate that object in the top-down view and determine the direction from which it would appear in the foreground.
The 24 marks around the table are evenly spaced, so each viewpoint has a fixed angular position, and viewpoints separated by a fixed offset always show the same objects shifted by that offset in the picture.
Sketch Q is anchored by a tall cylinder standing right in front of the viewer, and Sketch R is anchored by a cube in exactly that same near position, so whichever two numbers we pick, the angular gap between them has to match the actual gap between where the cylinder and the cube sit on the table.
Checking the table layout, the cylinder and the cube sit roughly a quarter of the way around the circle from each other, and only the pair 1 and 16 keeps that same spacing while also keeping the pyramid centred and behind in both sketches, exactly as drawn.
The other listed pairs either sit too close together or too far apart to reproduce that spacing, so they can be ruled out without checking every object in the picture.
So the sketches were taken from directions 1 and 16.
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Approach Solution -2
A cleaner way to check each option is to write out the order in which objects would be crossed by the eye, from nearest to farthest, for that viewpoint, and compare that order with the order actually drawn in each sketch.
Q:19, R:5: From 19 the near-to-far order comes out as cone, cylinder, pyramid, which does not match Sketch Q's order of cylinder, cone, pyramid, so this option is eliminated immediately.
Q:8, R:15: From 8 the order is cone, pyramid, cylinder, again not matching Sketch Q, so both halves of this option are wrong.
Q:1, R:16: From 1 the order is cylinder, cone, pyramid, second cylinder, which lines up exactly with Sketch Q. From 16 the order is cube, cone, cone, pyramid, which lines up exactly with Sketch R.
Q:24, R:15: From 24 the order does not begin with the tall cylinder, so it cannot match Sketch Q.
Since only direction 1 reproduces Sketch Q's near-to-far order and only direction 16 reproduces Sketch R's, the answer has to be Q:1, R:16.
