Question

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

Explanation:

Step1: Recall collinear points

Collinear points lie on the same line. From the figure, points $L$, $N$ lie on the same vertical - line. We can choose one more point on this line (but there are no other points on this line in the given figure). So, for part (a), we can say $N$, $L$ (and there are no other distinct points on this line in the given context).

Step2: Recall coplanar points

Coplanar points lie in the same plane. Points $M$, $P$, $H$, $J$, $K$ lie in plane $Z$. For part (b), we can choose $M$, $P$, $J$ as distinct points that are coplanar with $H$ (answers can vary as long as they are points in plane $Z$).

Step3: Find intersecting lines

If we consider a line $\overleftrightarrow{JP}$, we need to find another line that intersects it. In the plane $Z$, if we consider a line formed by two points, for example, $\overleftrightarrow{HK}$ (answers can vary), it can intersect $\overleftrightarrow{JP}$ in the plane $Z$.

Step4: Name a plane

A plane can be named by three non - collinear points in the plane. For plane $Z$, we can name it as plane $MPH$ (answers can vary as long as the three points are non - collinear and in the plane $Z$).

Answer:

(a) $L$ (no other distinct points on the line with $N$ and $L$ in the given figure)
(b) $M$, $P$, $J$ (answers may vary)
(c) $\overleftrightarrow{HK}$ (answers may vary)
(d) $MPH$ (answers may vary)