Question

in the figure below, points q, x, y, and s lie in plane p. points r and t 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) point q and line are coplanar. (c) t, , and are distinct points that are collinear. (d) $overleftrightarrow{xy}$ and are distinct lines that intersect.

Explanation:

Step1: Recall naming of planes

A plane can be named by any three non - collinear points on it. Points $Q$, $X$, and $Y$ are non - collinear points on plane $P$. So another name for plane $P$ is plane $QXY$.

Step2: Identify coplanar elements

Points $Q$, $X$, $Y$, and $S$ lie in plane $P$. The line $\overleftrightarrow{XY}$ lies in plane $P$. So point $Q$ and line $\overleftrightarrow{XY}$ are coplanar.

Step3: Find collinear points

Points $R$ and $T$ are on the same vertical line. So $T$, $R$, and any point on the line segment between them (for simplicity we can say $R$) are distinct points that are collinear.

Step4: Find intersecting lines

The line $\overleftrightarrow{XY}$ lies in plane $P$. The line $\overleftrightarrow{QS}$ also lies in plane $P$ and intersects $\overleftrightarrow{XY}$. So $\overleftrightarrow{XY}$ and $\overleftrightarrow{QS}$ are distinct lines that intersect.

Answer:

(a) $QXY$
(b) $\overleftrightarrow{XY}$
(c) $R$ (second blank can also be any point on the line segment between $T$ and $R$ like a mid - point etc, but $R$ is a simple choice); $R$
(d) $\overleftrightarrow{QS}$