Determinants are used to show that three points lie on the same line (are collinear). If = 0, then the points ( x1, y1), ( x2, y2), and ( x3, y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (-2, -1), (0, 9), (-6, -21) and collinear?

Question

amistre64 · Answer

determinants are defined for square matrixes ...

anonymous · Answer

i have no idea what im doing.

amistre64 · Answer

|dw:1395171133050:dw|

the 2 points are on a line, but the determinant of the matrix of their position vectors is not 0 since the position vectors are not parallel.

amistre64 · Answer

if, and only if, the points lie on a line that is thru the origin will the determinant of their position vectors be zero

amistre64 · Answer

personally, i would zero out a point .... and compare the other 2

(-2, -1),   (0, 9),   (-6, -21)
      -9         -9             -9
-------------------------
-2,-10        0,0      -6,-30

now we have something to determinant about

amistre64 · Answer

but since 3(-2,-10) = (-6,-30)  they are all in a line