Question

NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!

Planes S and R both intersect plane T . Which statements are true based on the diagram? Check all that apply.

Plane S contains points B and E.
The line containing points A and B lies entirely in plane T.
Line v intersects lines x and y at the same point.
Line z intersects plane S at point C.
Planes R and T intersect at line y.

Answer 1

Based on the diagram, we can assume that planes S and R are parallel.

"Plane S contains points B and E." (false)
 
S contains B. E is in R. S and R have no common point, so E cannot be in both R and S so E is not in S 

"The line containing points A and B lies entirely in plane T." (true)

a plane containing 2 points of a line, contains the line itself. A and B are in plane T, so the line through A and B is in T

"Line v intersects lines x and y at the same point." (false)

x is in S, y is in R and S and R are parallel, so they have no common point. Thus lines x and y have no common point.

"Line z intersects plane S at point C." (correct)

C is clearly the intersecting point of line z and plane S

"Planes R and T intersect at line y." (correct)

y is a line common to both planes R and T. The line of intersection of 2 planes is unique, so that unique line is y

Answer 2

In this problem, we have the intersection of planes. We have the figure that gives us all the information we need to solve each item. Therefore, the solution of this problem is as follows:

1. Plane S contains points B and E.

This is false as indicated in Figure 1. As you can see, It is true that point B (point in red color) lies on the plane S, but point E (point in green color) lies on the plane R and these two planes are not the same.

2. The line containing points A and B lies entirely in plane T.

This is true. This statement is indicated in Figure 2. So, the line containing points A and B has been remarked in red color. The point A has been remarked in orange color and the point B has been remarked in purple color. You can see that this line passes through this two points and lies on the plane T.

3. Line v intersects lines x and y at the same point.

This is false. The representation of this statement is illustrated in Figure 3. Line v has been remarked in red color and intersects the line x, that is remarked in pink color, at the point B remarked in orange color. On the other hand, line v intersects the line y, that is remarked in yellow color, at the point A remarked in blue color. So, point A and point B are not the same point.

4. Line z intersects plane S at point C.

This is true. This is shown in Figure 4. The point of intersection, between the line z remarked in red color and the plane S, is the point C remarked in green color.

5. Planes R and T intersect at line y.

This is true. You can see from Figure 5 that the line y remarked in red color is the intersection of the planes R and T. In fact, the intersection of two planes form a line.