Question

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?
A. Yes
B. No

Answer 1

i never learned this but apparently thats how you do it

Answer 2

-2 -1 1
0 9 1
-6 -21 1

Answer 3

\[\left[\begin{matrix}-2 & -1& 1 \\ 0 & 9 & 1\\ -6 & -21 &1\end{matrix}\right]\]

Answer 4

the determinant is not 0

Answer 5

nevermind the determinant IS 0

Answer 6

so yes it is colinear

Answer 7

yes i can give u a general expression if u like

Answer 8

idk what i did wrong in finding the det

Answer 9

parth did you get the answer you were looking for?

Answer 10

Fun fact: that determinant is actually used to find the area of a triangle given three points. And so when the determinant is zero, the area of the triangle is zero, meaning that the points are collinear.

Answer 11

two vector \[l_1a+l_2b,\\m_1a+m_2b,\\n_1a+n_2b, ~are~collinear ~if\\(m_1n_2-m_2n_1)+(n_1l_2-n_2l_1)+(l_1m_2-l_2m_1)=0\]
whivh is actually