Question

determine if the points (0,1),(2,3) and (4,5) are collinear​

Answer 1

Answer:

Yes, they are collinear.

Step-by-step explanation:

If three points $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ are collinear, the area of the triangle formed by the vertices of the point will be zero.

Hence, if $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ are collinear, then,

$\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0$

Hence, here,

$x_1=0,y_1=1\\x_2=2, y_2=3\\x_3=4, y_3=5$

Substituting these values in the formula,

$\frac{1}{2}|0(3-5)+2(5-1)+4(1-3)|=0$

$\frac{1}{2}|8-8|=0$

$=>0=0$,

Hence, LHS = RHS, and, the points are collinear.

Hope it helps.