Question

Determine whether the three given points are collinear. (3, 2), (4, 6), (0, 8) True: they are collinear False: they are not collinear

Answer 1

Answer:

They are not co-linear.

Step-by-step explanation:

For three point's to be co linear the slopes of the lines connecting them should be same

Mathematically we can write for $(x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})$

to be co-linear we should have

$\frac{y_{3}-y_{2}}{x_{3}-x_{2}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y_{3}-y_{1}}{x_{3}-x_{1}}$

Applying the given values we obtain

$\frac{y_{3}-y_{2}}{x_{3}-x_{2}}=\frac{8-6}{0-4}=-1/2\\\\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-2}{4-3}=3\\\\\frac{y_{3}-y_{1}}{x_{3}-x_{1}}=\frac{8-2}{0-3}=-2$

As we can see the values are not equal thus the points are not co-linear.