Question

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

Explanation:

Step1: Identify intersecting lines

Lines that intersect share a common point. Since $\overrightarrow{ED}$ is a line outside the plane and points $D$ and $E$ are not in plane $X$, a line in plane $X$ that can intersect it is $\overrightarrow{BD}$ (as $D$ is a common - point).

Step2: Identify collinear points

Collinear points lie on the same line. Points $A$, $B$, and $C$ are on the same vertical line in the plane, so $A$ (or $B$) and $C$ are collinear.

Step3: Rename the plane

A plane can be named by any three non - collinear points in the plane. Points $F$, $C$, and $A$ are non - collinear points in plane $X$, so plane $X$ can be called plane $FCA$.

Step4: Identify coplanar points

Coplanar points lie in the same plane. Points $A$, $B$, $C$, and $F$ all lie in plane $X$, so $A$, $B$, $C$, and $F$ are coplanar.

Answer:

(a) $\overrightarrow{BD}$
(b) $A$ (or $B$)
(c) $FCA$
(d) $B$, $C$, $F$