4. use the diagram to the right to name the following.
a) the intersection of lines ( l ) and ( m ). ______
b) another name for plane ( q ). ______
c) are points ( d ) and ( e ) collinear or coplanar? ______
d) how many times do planes ( p ) and ( q ) intersect? ______

Question

Accepted Answer

### Part a)
# Explanation:
## Step1: Recall intersection of lines
Two lines intersect at a point. From the diagram, lines $ l $ and $ m $ intersect at point $ E $.
# Answer:
$ E $

### Part b)
# Explanation:
## Step1: Recall naming a plane
A plane can be named by three non - collinear points on it. From the diagram, plane $ Q $ contains points $ E $, $ F $, $ G $, $ I $ (or other combinations). One possible name is plane $ EFG $ (or plane $ EFI $, plane $ EGI $, plane $ FGI $ etc., but looking at the diagram, points $ E $, $ F $, $ G $ are on line $ m $ and plane $ Q $, also point $ I $ is on plane $ Q $. A common way is to use three points, so plane $ Q $ can also be named as plane $ EFI $ (or other valid combinations, here we can see points $ E $, $ F $, $ I $ are on plane $ Q $) or more accurately, from the diagram, plane $ Q $ has points $ E $, $ F $, $ G $, $ I $, so another name could be plane $ EFG $ or plane $ EFI $, but a more precise one from the given points: plane $ Q $ can be named as plane $ EFI $ (or plane $ EGI $, but let's check the diagram. The plane $ Q $ has line $ m $ (with $ E $, $ F $, $ G $) and point $ I $. So a valid name is plane $ EFI $ (or plane $ EFGI $ but usually three non - collinear points. Since $ E $, $ F $, $ I $ are non - collinear (as $ F $ and $ E $ are on line $ m $, $ I $ is not on line $ m $), so plane $ Q $ can be named as plane $ EFI $ (or plane $ EGI $, plane $ FGI $, plane $ EFG $ is collinear? No, $ E $, $ F $, $ G $ are collinear on line $ m $, so we need three non - collinear points. So $ E $, $ F $, $ I $: $ E $ and $ F $ are on line $ m $, $ I $ is not on line $ m $, so they are non - collinear. So another name for plane $ Q $ is plane $ EFI $ (or plane $ EGI $, plane $ FGI $).
# Answer:
Plane $ EFI $ (or Plane $ EGI $, Plane $ FGI $, acceptable as long as three non - collinear points on plane $ Q $)

### Part c)
# Explanation:
## Step1: Recall collinear and coplanar
Collinear points lie on the same line, coplanar points lie on the same plane. Points $ D $ and $ E $ lie on line $ l $, so they are collinear. And since collinear points are always coplanar, but the question is asking are they collinear or coplanar. Since they lie on the same line, they are collinear.
# Answer:
Collinear

### Part d)
# Explanation:
## Step1: Recall intersection of planes
Two planes intersect in a line. So the number of times planes $ P $ and $ Q $ intersect is once (along the line $ l $).
# Answer:
Once (they intersect in a line, so the intersection is a line, meaning they intersect once in terms of the number of times their intersection occurs, i.e., they intersect along one line)

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QUESTION IMAGE

Question

Explanation:

Part a)

Step1: Recall intersection of lines

Step1: Recall naming a plane

Step1: Recall collinear and coplanar

Answer:

Part b)