Question

in the figure below, points l, j, m, n, and p lie in plane z. points h and k do not lie in plane z. for each part below, fill in the blanks to write a true statement. (a) and m are distinct points that are collinear. (b) n, , , and are distinct points that are coplanar. (c) suppose line $overleftrightarrow{hl}$ is drawn on the figure. then $overleftrightarrow{hl}$ and are distinct lines that intersect. (d) another name for plane z is plane

Explanation:

Step1: Recall collinear points definition

Collinear points lie on the same line. From the figure, points $N$ and $M$ are on the same line in plane $Z$. So for part (a), the answer is $N$.

Step2: Recall coplanar points definition

Coplanar points lie in the same plane. Points $N$, $J$, $L$, $M$, $P$ all lie in plane $Z$. For part (b), we can choose $J$, $L$, $P$ (answers can vary as long as they are points in plane $Z$ other than $N$). Let's choose $J$, $L$, $P$.

Step3: Find intersecting line

We need to find a line that intersects $\overleftrightarrow{HL}$. Point $J$ is a point that can be used to form a line that intersects $\overleftrightarrow{HL}$. If we consider line $\overleftrightarrow{HJ}$, it will intersect $\overleftrightarrow{HL}$ at point $H$. So for part (c), the answer is $\overleftrightarrow{HJ}$.

Step4: Name the plane

A plane can be named by three non - collinear points in the plane. Points $J$, $L$, $M$ are non - collinear points in plane $Z$. So for part (d), another name for plane $Z$ is plane $JLM$ (answers can vary as long as they are three non - collinear points in plane $Z$).

Answer:

(a) $N$
(b) $J$, $L$, $P$
(c) $\overleftrightarrow{HJ}$
(d) $JLM$