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, m, and p 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 coplanar points concept

Coplanar points lie in the same plane. Points $M, P, H, J, K$ lie in plane $Z$. So we can choose any 3 of them. Let's choose $J$, $K$, $P$.

Step2: Recall intersecting - lines concept

We need to find a line that intersects $\overleftrightarrow{JP}$. $\overleftrightarrow{ML}$ (where $M$ is in plane $Z$ and $L$ is outside) can intersect $\overleftrightarrow{JP}$ as they are in different - relative positions in 3 - D space.

Step3: Recall naming a plane

A plane can be named by any three non - collinear points in the plane. We can use $M$, $H$, $K$ to name plane $Z$.

Answer:

(a) False (since $N$ is not in plane $Z$ and $M, P$ are in plane $Z$, they are not collinear)
(b) $J$, $K$, $P$
(c) $\overleftrightarrow{ML}$
(d) $MHK$