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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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` .

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial