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) another name for plane x is plane □. (b) a, □, □, and □ are distinct points that are coplanar. (c) □ and c are distinct points that are collinear. (d) \overleftrightarrow{ed} and □ are distinct lines that intersect.

Explanation:

Step1: Name the plane

A plane can be named by three non - collinear points. Points \(F\), \(C\), \(B\) are non - collinear and lie on plane \(X\). So another name for plane \(X\) is plane \(FBC\) (any three non - collinear points from \(F\), \(C\), \(B\), \(A\) can be used).

Step2: Find coplanar points

Since points \(F\), \(C\), \(B\), \(A\) lie in plane \(X\), \(A\), \(B\), \(C\), \(F\) are distinct points that are coplanar.

Step3: Find collinear points

Points \(B\) and \(C\) lie on the same line (the vertical line in the plane \(X\)). So \(B\) and \(C\) are distinct points that are collinear.

Step4: Find intersecting lines

Line \(\overleftrightarrow{ED}\) (the horizontal line) and line \(\overleftrightarrow{AC}\) (the vertical line in plane \(X\)) intersect at point \(B\).

Answer:

(a) \(FBC\) (or \(FBA\), \(FCA\), \(BCA\))
(b) \(B\), \(C\), \(F\)
(c) \(B\)
(d) \(\overleftrightarrow{AC}\)