Question

refer to the figure at the right. 43. name two collinear points. 44. how many planes appear in the figure? 45. do plane a and plane mnp intersect? explain. 46. in what line do planes a and qrv intersect? 47. are points t, s, r, q, and v coplanar? explain. 48. are points t, s, r, q, and w coplanar? explain.

Explanation:

Step1: Recall collinear - points definition

Collinear points lie on the same line. Points T and S lie on the same line, so they are collinear.

Step2: Count planes in the figure

The planes in the figure are plane A, plane QRV, plane MNP, plane PUV, plane TSRQ, plane TUVW, so there are 6 planes.

Step3: Analyze plane - plane intersection for plane A and plane MNP

Plane A and plane MNP are parallel. Parallel planes do not intersect, so they do not intersect.

Step4: Determine intersection line of planes A and QRV

The intersection of plane A and plane QRV is the line QR.

Step5: Check coplanarity of points T, S, R, Q, V

Points T, S, R, Q, V all lie on the rectangular - shaped face of the prism which is a plane, so they are coplanar.

Step6: Check coplanarity of points T, S, R, Q, W

Point W is not on the same plane as points T, S, R, Q. So they are not coplanar.

Answer:

1. T and S
2. 6
3. No, they are parallel.
4. Line QR
5. Yes, they lie on the same plane.
6. No, point W is not on the same plane as the others.