Question

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

Explanation:

Step1: Recall naming of a plane

A plane can be named by any three non - collinear points on the plane. Points $T$, $R$, $X$ are non - collinear points on plane $P$, so plane $P$ can be named as plane $TRX$.

Step2: Recall collinear points

Collinear points lie on the same line. Points $X$ and $Y$ lie on the same line, so $X$ and $Y$ are collinear.

Step3: Recall coplanar points and lines

A point and a line are coplanar if they lie on the same plane. Line $\overleftrightarrow{RX}$ lies on plane $P$ and point $T$ lies on plane $P$, so point $T$ and line $\overleftrightarrow{RX}$ are coplanar.

Step4: Recall intersecting lines

If we draw line $\overleftrightarrow{TS}$, and consider line $\overleftrightarrow{RX}$, they are distinct lines that will intersect (since they are in the same plane and not parallel).

Answer:

(a) $TRX$
(b) $X$
(c) $\overleftrightarrow{RX}$
(d) $\overleftrightarrow{RX}$