Math Problem Statement
Solution
Let's go through the questions based on the image:
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Question 5: "Name the intersection of lines and ."
- From the figure, lines and intersect at point .
- Answer: The intersection of lines and is .
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Question 6: "Give another name for line ."
- Line passes through points and , so we can name the line using these two points.
- Answer: Another name for line is line .
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Question 7: "Name a point that is not contained in any of the three lines , , or ."
- Points on line are . Points on line are . Points on line are . Therefore, point is not on any of these lines.
- Answer: Point is not contained in any of the three lines.
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Question 8: "Give another name for plane ."
- A plane can be named using any three non-collinear points. In this case, we could use or include another point on the plane such as .
- Answer: Another name for plane is plane .
Now for the geometric models:
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Geometric term modeled by the fence (image 9):
- The fence represents a line because it extends straight in one dimension.
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Geometric term modeled by the beads on the string (image 10):
- The beads represent points because they are distinct, non-dimensional locations along the string.
Would you like more details or have any questions? Here are 5 related questions to explore the concepts further:
- What are the defining properties of a plane in geometry?
- How many points are required to uniquely define a line?
- Can two planes intersect at more than one line? Why or why not?
- What is the significance of collinear points when naming a line?
- How do you distinguish between a point, a line, and a plane in 3D space?
Tip: When naming a line, you can use any two distinct points on that line. For a plane, you can use three non-collinear points.
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Math Problem Analysis
Mathematical Concepts
Geometry
Lines
Planes
Points
Formulas
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Theorems
Intersection of Lines
Naming of Planes and Lines
Suitable Grade Level
Grade 7-9
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