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) q and r are distinct points that are collinear. (b) point z and line qr are coplanar. (c) suppose line zy is drawn on the figure. then zy and xr are distinct lines that intersect. (d) another name for plane p is plane xzr.

Explanation:

Step1: Recall collinear - points definition

Collinear points lie on the same line. Since $Q$ and $R$ are on the same line in the figure, they are collinear.

Step2: Recall coplanar - point and line definition

Coplanar means lying in the same plane. Point $Z$ and line $\overleftrightarrow{QR}$ both lie in plane $P$, so they are coplanar.

Step3: Analyze intersecting - lines

If line $\overleftrightarrow{ZY}$ is drawn, it will intersect line $\overleftrightarrow{XR}$ as they are in different - oriented lines in the 3 - D space related to plane $P$.

Step4: Name a plane

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

Answer:

(a) $Q$ and $R$ are distinct points that are collinear.
(b) Point $Z$ and line $\overleftrightarrow{QR}$ are coplanar.
(c) Suppose line $\overleftrightarrow{ZY}$ is drawn on the figure. Then $\overleftrightarrow{ZY}$ and $\overleftrightarrow{XR}$ are distinct lines that intersect.
(d) Another name for plane $P$ is plane $XZR$.