refer to the figure at the right. indicate whether each statement is true or false. a. points a, b, and c are collinear. false not on the same line b. the intersection of plane abc and line m is point p. c. line ℓ and line m do not intersect. d. points a, p, and b can be used to name plane u. e. line ℓ lies in plane acb. refer to the figure. 1. name a line that contains points t and p.

Question

Accepted Answer

### Part a:
# Explanation:
## Step1: Recall collinear points
Collinear points lie on the same line. From the figure (assuming standard plane - line - point setup), if A, B, C are in plane ABC, but if they don't lie on a single line, they are non - collinear. So the statement "Points A, B, and C are collinear" is False.
## Step2: Conclusion
Based on the definition of collinear points and the figure (implied non - collinear nature of A, B, C), the statement is false.

# Answer: False

### Part b:
# Explanation:
## Step1: Intersection of plane and line
The intersection of a plane and a line is either a point (if the line is not entirely in the plane) or the line itself (if the line is in the plane). From the figure, plane ABC and line $m$ intersect at point P (as per the diagram's context). So the statement "The intersection of plane ABC and line $m$ is point P" is True.
## Step2: Conclusion
Using the concept of plane - line intersection, the statement is true.

# Answer: True

### Part c:
# Explanation:
## Step1: Intersection of two lines
Two lines in a plane (or in space) either intersect (at a point) or are parallel (in a plane) or skew (in space). From the figure, line $\ell$ and line $m$ intersect at a point (implied by the diagram's structure). So the statement "Line $\ell$ and line $m$ do not intersect" is False.
## Step2: Conclusion
Based on the visual (or implied) intersection of line $\ell$ and line $m$, the statement is false.

# Answer: False

### Part d:
# Explanation:
## Step1: Naming a plane
A plane can be named by three non - collinear points. Points A, P, and B: if they are non - collinear (from the figure's context), they can be used to name plane $u$ (assuming plane $u$ contains these points). So the statement "Points A, P, and B can be used to name plane $u$" is True.
## Step2: Conclusion
Using the rule of naming a plane with three non - collinear points, the statement is true.

# Answer: True

### Part e:
# Explanation:
## Step1: Line in a plane
A line lies in a plane if all its points are in the plane. Plane ACB (or ABC) and line $\ell$: from the figure, if line $\ell$ is not entirely within plane ACB (maybe it intersects the plane at a point or is skew), then the statement "Line $\ell$ lies in plane ACB" is False.
## Step2: Conclusion
Based on the concept of a line lying in a plane and the figure's context, the statement is false.

# Answer: False

### Part 1:
# Explanation:
## Step1: Identify the line with T and P
From the figure (the lower - left diagram), we look for the line that contains both points T and P. By observing the lines in the diagram, we can see that there is a line (let's assume it's line $j$ or another labeled line, but from the diagram's structure) that passes through T and P. Let's assume the line is line $j$ (or based on the diagram's labels, if T and P are on a line, we name that line. For example, if the line is labeled as line $TP$ or another name, but from the visual, the line containing T and P can be named as line $j$ (or the specific line as per the diagram). Let's say the line is line $j$ (or the line passing through T and P, named as line $TP$ or the labeled line in the diagram).
## Step2: Conclusion
By looking at the figure, the line containing points T and P is (for example, if the line is labeled as line $j$ or the line through T and P, we name it. Let's assume the line is line $j$ or the line $TP$, but from the diagram, the line containing T and P is the line that connects them, say line $m$ (depending on the diagram's actual labels). But generally, we name the line by the two points, so line $TP$ or the labeled line in the diagram.

# Answer: Line $TP$ (or the specific line label from the diagram, e.g., if it's line $j$, then line $j$)

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QUESTION IMAGE

Question

Explanation:

Part a:

Step1: Recall collinear points

Step2: Conclusion

Step1: Intersection of plane and line

Step2: Conclusion

Step1: Intersection of two lines

Step2: Conclusion

Answer:

Part b: