Question

consider the figure shown.
what is another name for the plane containing points b, c, and d?
a plane f
b plane af
c plane cb
d plane r
which term describes the set of points e, f, and d?
a collinear
b coplanar

Explanation:

First question:

Step1: Recall plane naming rules

A plane can be named by a single capital letter (not a point) or by three non - collinear points on the plane. In the figure, the plane containing \(B\), \(C\), and \(D\) is also named plane \(R\) (since \(R\) is the label for that plane).

• Option A: Plane \(F\) is incorrect because \(F\) is a point, not a plane name in the sense of a single - letter plane name (a plane named by a single letter should be a script or non - point label, here \(R\) is the plane label).
• Option B: Plane \(AF\) is incorrect because \(A\) is not on the same plane as \(B\), \(C\), and \(D\) ( \(A\) is on line \(r\) which is perpendicular to the plane containing \(B\), \(C\), \(D\)).
• Option C: Plane \(CB\) is incorrect because we need at least three non - collinear points to name a plane in the point - naming convention (or a single plane label), and \(CB\) only has two points.

Second question:

Step1: Recall collinear and coplanar definitions

• Collinear points lie on the same straight line.
• Coplanar points lie on the same plane.

Points \(E\), \(F\), and \(D\) lie on the same plane (plane \(R\)), but they are not on the same straight line.

Answer:

1. D. plane \(R\)
2. B. coplanar