Question

determine whether the points are A(0,2),B(1,-0.5),C(2,-3) collinear and non collinear ​

Answer 1

❖EXPLANATION

❖Given to find whether the points are collinear or non- collinear

A= ( 0, 2)

B = ( -1, 0.5)

C = (2 , -3)

❖Solution :-

If the area is 0 then the given points are collinear. If the area is not 0 then the given points are non-collinear.

❖Area of triangle = 1/2 |x1(y2-y3) + x2(y3-y1) + x3(y1-y2) |

Substituting the values ,

x1 = 0

x2 = 1

x3 = 2

y1 = 2

y2 = -0.5

y3 = -3

❖Area of triangle = 1/2 |x1(y2-y3) + x2(y3-y1) + x3(y1-y2) |

= 1/2 | 0[-0.5-(-3) ]+ 1(-3-2) +2[2-(-0.5)] |

= 1/2 | 0 +1(-5) +2[2+0.5] |

= 1/2 | 0 -5 +2(2.5)|

= 1/2 | -5 +5|

= 1/2|0|

= 1/2 (0)

= 0

❖Since , Area is 0 So, the given points are collinear