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 $overleftrightarrow{}$ are distinct lines that intersect. (d) another name for plane z is plane .

Explanation:

Step1: Recall collinear and coplanar definitions

Collinear points lie on the same line, coplanar points lie on the same plane.

Step2: Analyze part (b)

From the figure, since points \(M\), \(P\), \(H\), \(J\), \(K\) are in plane \(Z\), we can choose \(M\), \(J\), \(K\) (answers can vary as long as they are in plane \(Z\)) as distinct points that are coplanar.

Step3: Analyze part (c)

We need to find a line that intersects \(\overleftrightarrow{JP}\). A possible line is \(\overleftrightarrow{ML}\) (as it passes through the plane and can intersect \(\overleftrightarrow{JP}\)).

Step4: Analyze part (d)

A plane can be named by three non - collinear points in the plane. So plane \(Z\) can also be named plane \(MPH\) (answers can vary as long as the three points are non - collinear in plane \(Z\)).

Answer:

(b) \(M\), \(J\), \(K\) (answers may vary)
(c) \(\overleftrightarrow{ML}\) (answers may vary)
(d) \(MPH\) (answers may vary)