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Let $S$ be the set of points $(a,b)$ in the coordinate plane, where each of $a$ and $b$ may be $-1$, 0, or 1. How many distinct lines pass t
Question
Let $S$ be the set of points $(a,b)$ in the coordinate plane, where each of $a$ and $b$ may be $-1$, 0, or 1. How many distinct lines pass through at least two members of $S$
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Mathematics
3 years
2021-08-02T09:10:12+00:00
2021-08-02T09:10:12+00:00 1 Answers
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Answer:
20 Lines
Step-by-step explanation:
According to the Question,
Now, the total pairs of points which can be formed is 9
And, the line passing through 2 such points 9c2 = 9! / (2! x 7!) = 9×4 ⇒ 36
Here, We have overcounted all of the lines which pass through three points.
And, each line that passes through three points will have been counted 3c2 = 3! / 2! ⇒ 3 times
Now, the sides of the square consist of 3 points. We have counted each side thrice, so 4*2 are repeated.