# The points A(-m,1), B(1,m), C(0,1) lie in straight line if m=? Solve with determinants

You should use the test for collinear points, hence you should suppose that the points are vertices of triangle and you should evaluate the area of this triangle using determinants.

If determinants is zero, then the points are collinear and there is no triangle, but a line.

You need to form the determinant such that:

`[[-m,1,1],[1,m,1],[0,1,1]] `

The problem provides the information that these points are collinear, hence the determinant needs to be zero such that:

`[[-m,1,1],[1,m,1],[0,1,1]] = 0`

You need to evaluate the determinant such that:

`-m^2 + 1  + m - 1 = 0 =gt m^2 - m = 0`

Factoring out m yields:

`m(m-1) = 0 =gt m_1 = 0`

`m-1=0 =gt m_2=1`

Hence, evaluating m yields that two values for m make check  the collinear condition such that `m_1 = 0`  and `m_2=1` .

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