please explain:
collinearity
proving collinearity
for the high school level
Hello, ligekron!
Please explain: (1) Collinearity, (2) Proving collinearity
for the high school level
Since your heading says "Vectors", I assume a vector approach is in order.
Three points $\displaystyle A,\,B,\,C$ are collinear (lie on a straight line)
if any two of their vectors $\displaystyle \{\overrightarrow{AB},\;\overrightarrow{BC},\; \overrightarrow{AC}\}$ are scalar multiples of each other.
$\displaystyle \text{Example: }\;A(2,3),\;B(3,5),\;C(5,9)$
$\displaystyle \text{Let }\vec{u} \:=\:\overrightarrow{AB} \:= \:\langle 3,5\rangle - \langle 2,3\rangle \:=\:\langle 1,2\rangle $
$\displaystyle \text{Let }\vec{v}\:=\:\overrightarrow{BC} \:=\:\langle 5,9\rangle - \langle 3,5\rangle \:=\:\langle 2,4\rangle$
$\displaystyle \text{Since }\vec{v} = 2\vec{u}\text{, points }A,\;B,\,C\text{ are collinear.}$