Question

Use the diagram on the right. How many planes contain both the line and the point

Answer 1

Part (a)

Answer: 0

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Explanation:

Point P is part of 3 planes or faces of this triangular prism:

• plane PEF (the front slanted plane)
• plane PEH (the left triangular face)
• plane PHG (the back rectangular wall)

Notice how each three letter sequence involves "P", though this isn't technically always necessary. I did so to emphasize how point P is involved with these planes.

Each of the three planes mentioned do not involve line FG

• Plane PEF only deals with point F
• Plane PEH doesn't have any of F or G involved
• plane PHG only involves G

So there are no planes that contain line FG and point P.

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Part (b)

Answer: 0

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Explanation:

It's the same idea as part (a) earlier. The planes involving point G are

• plane GQF  (triangular face on the right)
• plane GFE (bottom rectangular floor)
• plane GHP (back rectangular wall)

None of these planes have line EP going through them.

As an alternative, we could reverse things and focus on all of the planes connected to line EP. Those 2 planes are

• plane PEH (triangular face on the left)
• plane PEF (front slanted rectangular face)

None of these planes have point G located in them.