Math, asked by prarthana46, 1 year ago

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

Attachments:

Answers

Answered by umang2299
3
the slope of any 2 pair of points is same then they are collinear..

umang2299: hi
umang2299: can you please help me in solution of one question
Answered by qwsuccess
1

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.

Similar questions