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

Explanation:

Step1: Recall definitions

Collinear points are on the same line, coplanar points are in the same plane.

Step2: Analyze part (a)

We need three distinct non - coplanar points. Since \(N\) is outside plane \(Z\), we can choose two points from plane \(Z\) like \(M\) and \(P\). So \(N\), \(M\), and \(P\) are distinct points.

Step3: Analyze part (b)

From the figure, \(H\), \(J\), and \(K\) lie on the same line, so they are collinear.

Step4: Analyze part (c)

If \(\overrightarrow{JP}\) is drawn, a line that intersects it and is in the same plane \(Z\) could be \(\overrightarrow{HK}\). They are distinct lines in plane \(Z\).

Step5: Analyze part (d)

A plane can be named by three non - collinear points in the plane. So plane \(Z\) can also be called plane \(MHK\) (using non - collinear points \(M\), \(H\), and \(K\) in plane \(Z\)).

Answer:

(a) \(N\), \(M\), \(P\)
(b) \(H\), \(J\), \(K\)
(c) \(\overrightarrow{HK}\)
(d) \(MHK\)