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Condition for Two Lines to Be Perpendicular

There are 12 ...

Question

There are 12 points in a plane of which 5 are collinear. Find (i) the number of straight lines obtained by joining these points in pairs (ii) the number of triangles that can be formed with vertices at these points.

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Solution

(i) No. of lines = $^{12} C_{2}$ - $^{5} C_{2}$ + 1 = 66 - 10 + 1 = 57.
(ii) No. of $Δ^{s}$ = $^{12} C_{3}$ - $^{5} C_{3}$ = 220 - 10 = 210.

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Condition for Two Lines to Be Perpendicular

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