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Does the point belong to the line?

Statement. Line r passes through A(0, 3, 0) and B(8, 3, 4). Check whether point P(4, 3, 2) belongs to r.

Step-by-step solution

1. Draw A and B with both projections and join them: r' passes through A' and B', and r'' through A'' and B''.
2. Place P' and P''.
3. A point belongs to the line if BOTH projections fall on the matching projections of the line.
4. P' falls on r' and P'' on r'', so P does belong to r. It is also the midpoint of AB.

Result

Yes, it belongs: P lies on r (it is the midpoint of AB).

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