Question

in the figure below, points x, z, q, r, and s lie in plane p. points t and y do not lie in plane p. for each part below, fill in the blanks to write a true statement. (a) and r are distinct points that are collinear. (b) point z and line are coplanar. (c) suppose line \\(\overleftrightarrow{zy}\\) is drawn on the figure. then \\(\overleftrightarrow{zy}\\) and are distinct lines that intersect. (d) another name for plane p is plane .

Explanation:

Step1: Recall collinear points definition

Collinear points lie on the same line. Points $Q$ and $R$ lie on the same line in plane $P$.

Step2: Recall coplanar definition

Coplanar means lying in the same plane. Point $Z$ and line $\overleftrightarrow{QR}$ (or $\overleftrightarrow{QS}$, $\overleftrightarrow{RS}$ etc. that lie in plane $P$) are in plane $P$. Let's choose $\overleftrightarrow{QR}$.

Step3: Identify intersecting lines

If line $\overleftrightarrow{ZY}$ is drawn, it will intersect a line in plane $P$. Since $Z$ is in plane $P$, a line like $\overleftrightarrow{XR}$ which also lies in plane $P$ will intersect $\overleftrightarrow{ZY}$ at point $Z$.

Step4: Name a plane

A plane can be named by three non - collinear points in the plane. Points $X$, $Z$, $R$ are non - collinear points in plane $P$, so plane $P$ can be named plane $XZR$.

Answer:

(a) $Q$
(b) $\overleftrightarrow{QR}$
(c) $\overleftrightarrow{XR}$
(d) $XZR$