Question

1. name the line and plane shown in the diagram.

options: $overline{ab}$ and plane abd; $overline{ac}$ and plane abd; $overline{ba}$ and plane dc; $overline{ab}$ and plane da

Explanation:

1. Analyze the line: The line passes through points A and B, so it should be named \(\overline{AB}\) (or \(\overleftrightarrow{AB}\) for a line, but the options use segment notation which can represent the line here).
2. Analyze the plane: The plane contains points A, B, and D (since D is in the same plane as the line AB). So the plane is plane ABD.
3. Check the options:

• First option: \(\overline{AB}\) and plane ABD – matches our analysis.
• Second option: \(\overline{AC}\) – point C is not on the line, so incorrect.
• Third option: \(\overline{BA}\) (same as \(\overline{AB}\) but plane DC is incorrect as D and C are not defining the plane with the line).
• Fourth option: plane DA is incorrect as the plane contains A, B, D.

Answer:

A. \(\overline{AB}\) and plane ABD