Question

show the points (0,-3/2),(1,-1 )and (2,-1/2) are collinear

Answer 1

the slope of any 2 pair of points is same then they are collinear..

Answer 2

Given: Three points (0,-3/2), (1,-1 ) and (2,-1/2)

To show: The given point are collinear

Solution:

∵ Three ponits $(x_{1}, y_{1}), ( x_{2}, y_{2}) \ and \ (x_{3}, y_{3} )$ are collinear iff

$x_{1}( y_{2} -y_{3}) \ + \ x_{2}( y_{3} - y_{1}) \ + \ x_{3}( y_{1}- y_{2} )=0$

Now, according to the given question,

$x_{1} = 0, y_{1} = \frac{-3}{2} \\x_{2} = 1 , y_{2} = -1\\ x_{3} = 2, y_{3} = \frac{-1}{2}$

⇒ $x_{1}( y_{2} -y_{3}) \ + \ x_{2}( y_{3} - y_{1}) \ + \ x_{3}( y_{1}- y_{2} )= 0(-1 + \frac{1}{2}) + 1(\frac{-1}{2} + \frac{3}{2} ) + 2(\frac{-3}{2} + 1)$

⇒ $0 + 1(\frac{-1 \ + \ 3}{2}) + 2(\frac{-3 \ + \ 2}{2})$

⇒ $0 + 1(\frac{2}{2}) + 2(\frac{-1}{2})$

⇒ $0 + 1 -1 = 0$

Hence, shown that the given points are collinear.