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 the plane. Points $Q$, $X$, $Y$ are non - collinear points on plane $P$, so another name for plane $P$ is plane $QXY$.

Step2: Identify coplanar line with point $Q$

Lines on the same plane as a point are coplanar with that point. Line $\overleftrightarrow{XY}$ lies in plane $P$ where point $Q$ is, so point $Q$ and line $\overleftrightarrow{XY}$ are coplanar.

Step3: Find collinear points with $T$

Points on the same line are collinear. Points $R$ and $T$ lie on the same vertical line, so $T$, $R$, and any other point on that line (for example, a point between $R$ and $T$ if there was one marked) are collinear. Here we can say $T$, $R$.

Step4: Find intersecting line with $\overleftrightarrow{XY}$

Lines that cross each other are intersecting. Line $\overleftrightarrow{QS}$ intersects $\overleftrightarrow{XY}$ at a point in plane $P$.

Answer:

(a) $QXY$
(b) $\overleftrightarrow{XY}$
(c) $R$ (second blank can be any other point on the line containing $T$ and $R$, here we use $R$)
(d) $\overleftrightarrow{QS}$