Question

in the figure below, points a, e, f, and c lie in plane x. points b and d do not lie in plane x. for each part below, fill in the blanks to write a true statement. (a) b, blank, and blank are distinct points that are collinear. (b) fc and blank are distinct lines that intersect. (c) e, blank, and blank are distinct points that are coplanar. (d) another name for plane x is plane blank.

Explanation:

Step1: Identify collinear points in plane X

Points A, C are collinear and in plane X. So for (a), we can say B, A, and C are distinct points that are collinear.

Step2: Identify intersecting lines in plane X

Lines $\overrightarrow{FC}$ and $\overrightarrow{EA}$ (assuming a line through E and A can be considered) are distinct lines that intersect in plane X. So for (b), $\overrightarrow{FC}$ and $\overrightarrow{EA}$ are distinct lines that intersect.

Step3: Identify non - collinear coplanar points in plane X

Points E, F, and A are distinct points that are coplanar (in plane X) and non - collinear. So for (c), E, F, and A are distinct points that are coplanar.

Step4: Name the plane differently

A plane can be named by any three non - collinear points in the plane. Points A, E, F are non - collinear points in plane X. So another name for plane X is plane AEF.

Answer:

(a) B, A, and C
(b) $\overrightarrow{FC}$ and $\overrightarrow{EA}$
(c) E, F, and A
(d) plane AEF