Question

Determine if the points (1,5),(2,3)and(-2,-11)are collinear

Answer 1

Using the Distance Formula ,

1st and 2nd distance ,

=> \sqrt{(1-2)^{2}+(5-3)^{2}}

=> \sqrt{1+4}

=>\sqrt{5}

2nd and 3rd ,

=>\sqrt{(2+2)^{2}+(3+11)^{2}}

=>\sqrt{16+196}

=>\sqrt{212}

1st and 3rd point .

=>\sqrt{(1+2)^{2}+(5+11)^{2}}

=>\sqrt{9+256}

=>\sqrt{265 }

so ,

Ist and 2nd + 2nd and 3rd = 1st and 3rd is law of collinearity ,

Lets check ,

5+ 212 = 256

217 not equal 256

Hence ,

It does not satisfy the condition , Hence they are not collinear .

Answer 2

suppose A =(1 5),B=(2,3),C(-2,-11)

slope of AB= 3-5÷2-1=2

slope of BC=-11-3÷ -2-2=7÷2