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: Name the plane

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: Find a coplanar line with point Q

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

Step3: Find collinear points with T

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 labeled, but since there isn't we just use $R$) are collinear.

Step4: Find intersecting lines

Line $\overleftrightarrow{XY}$ and line $\overleftrightarrow{QS}$ intersect at a point (not labeled explicitly but they cross in the plane).

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) $\overleftrightarrow{QS}$