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InterviewSolution
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There are ten points in the plane, no three of which are coolinear. How many different lines can be drawn through these points ? |
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Answer» There are ten points `P_(1), P_(2),.., P_(10)`. For one line two points are required. Through point `P_(1)` there will be 9 lines when `P_(1)` is joined with any of the nine other points. Similarly, there will be nine lines passing through each point. So, number of lines is `9xx10` or 90. But there is double counting in above answer. Why ? One of the nine lines passing through point `P_(1) " is" P_(1) P_(2). "But" P_(1) P_(2)` is also one of the lines passing through point `P_(2)`. Thus, line `P_(1)P_(2)` and similarly each line is counted twice. Therefore, actual number of lines is `(90)/(2)=45`. |
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