Question

use the diagram to answer the following questions.
what points appear in the figure? p, s, i, m, n, o, u, r, q, l
how many lines appear in the figure? 5
how many planes appear in the figure? 2
name three collinear points. m, n, o
name four non - coplanar points. p, t, u, r
name another name for line e. mn
name the intersection of (overrightarrow{pq}) and (overrightarrow{mo}). n
name the intersection of plane k and line c. r
name another name for plane l. mno
name the ray for (overrightarrow{pq}). qp

Explanation:

Step1: Identify points

By observing the figure, we can list the points \(P, S, M, N, O, U, R, Q, L, T\) that appear in the figure.

Step2: Count lines

We can see lines \(e\), \(c\), \(d\), and two other lines (formed by the intersections and connections in the figure), so there are 5 lines.

Step3: Count planes

There are two planes labeled \(K\) and \(L\).

Step4: Find collinear points

Points \(M\), \(N\), \(O\) lie on the same line \(e\), so they are collinear.

Step5: Find non - coplanar points

For example, points \(R\), \(T\), \(U\), \(P\) are non - coplanar as \(P\) is in plane \(K\) and \(R\), \(T\), \(U\) have a combination that shows they don't all lie in one plane.

Step6: Name line \(e\)

One way to name line \(e\) is \(\overleftrightarrow{MN}\).

Step7: Find intersection of \(\overrightarrow{PQ}\) and \(\overrightarrow{MO}\)

The intersection point is \(N\).

Step8: Find intersection of plane \(K\) and line \(c\)

The intersection point is \(R\).

Step9: Name plane \(L\)

One way to name plane \(L\) is by three non - collinear points in it like \(MNO\).

Step10: Name \(\overrightarrow{PQ}\)

One way is \(\overrightarrow{QP}\) (as a vector has a direction).

Answer:

Points: \(P, S, M, N, O, U, R, Q, L, T\); Lines: 5; Planes: 2; Collinear points: \(M, N, O\); Non - coplanar points: \(R, T, U, P\) (example); Name for line \(e\): \(\overleftrightarrow{MN}\); Intersection of \(\overrightarrow{PQ}\) and \(\overrightarrow{MO}\): \(N\); Intersection of plane \(K\) and line \(c\): \(R\); Name for plane \(L\): \(MNO\); Name for \(\overrightarrow{PQ}\): \(\overrightarrow{QP}\)