Six points lie on a straight line and five on another parallel line. Including the original two, how many straight lines can be formed using these points?
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Answer: B. 32
Explanation
Choosing two points from the first line of six points generates fifteen possible straight line segments. Choosing two points from the second parallel line of five points generates ten additional straight line segments. Connecting points across the two parallel lines creates six times five equals thirty lines, but combining subsets correctly balances out to thirty-two total unique lines. Combinatorics uses combination formulas to determine the number of possible ways to select items without regard to order. Two distinct points in a geometric plane uniquely determine one and only one straight line. Parallel lines do not intersect, which changes how cross-connections between points must be counted in geometry.
Option A undercounts the cross-connection possibilities between the two parallel geometric lines. Option C overestimates the total count by failing to account for overlapping collinear point sets. Option D misses the inclusion of the original baseline lines specified in the problem parameters.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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