The number of different straight lines that are formed with A (2,3), B(3,4), C(5,6), D(3,7) are

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Solution

The correct option is D
4

Given points are A (2,3), B(3,4), C(5,6), D(3,7)

Equation of line $¯ ¯¯¯¯¯¯ ¯ A B$ is x-y+1=0

C(5,6) lies on this line, but not D(3,7)

$∴$ 3 collinear points and one different point are given

$∴$ No. Of lines that are formed =4

Note:

No. of lines that are formed with 'n' non-collinear = $^{n} C_{2}$

Out of 'n' points if 'p' points are collinear then no. of lines that are fromed = $^{n} C_{2} -^{P} C_{2} + 1$

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