Concept explainers
(a)
To Find: The number of distinct segments that are formed by the four collinear points by fiver collinear points.
(a)
Answer to Problem 48PPS
The number of distinct segment that are formed by the four collinear points is 6 and by five collinear points is 10.
Explanation of Solution
Given:
The given diagram is shown in Figure 1
Figure 1
Calculation:
Consider the diagram that shows the collinear line segment is shown in Figure 2
Figure 2
The four collinear points form the 6 distinct segments as
The figure to represent the five collinear point is shown in Figure 2
Figure 3
The five collinear points form the 10 distinct segments as
(b)
To Find: Theconjecture about the number of distance segments that is formed by the n collinear points.
(b)
Answer to Problem 48PPS
The pattern for the sequence is
Explanation of Solution
Consider the sequence is,
Then, the pattern for the sequence is
(c)
To Find: The test for the conjecture by finding the number of distinct segments that are formed by the six points.
(c)
Answer to Problem 48PPS
The six collinear points form the 15 distinct segments.
Explanation of Solution
Consider the figure to show the six collinear points is shown in Figure 4
Figure 4
The six collinear points form is
Chapter 2 Solutions
Geometry, Student Edition
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