Question

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

Answer 1

$\bf\huge\boxed{\boxed{\bf\huge\:Hello\:Mate}}}$

$\bf\huge Let A(1 , 5) , \: B(2 , 3) , \: C(-2 , -11)$

$\bf\huge AB= \sqrt{(2 - 1)^2 + (3 - 5)^2}$

$\bf\huge = \sqrt{1^2 + (-2)^2}$

$\bf\huge = \sqrt{1 + 4} = \sqrt{5}$

$\bf\huge BC = \sqrt{(-2 - 2)^2 + (-11 - 3)^2}$

$\bf\huge BC = \sqrt{(-4)^2 + (-14)^2}$

$\bf\huge BC = \sqrt{16 + 196}$

$\bf\huge BC = \sqrt{212}$

$\bf\huge AB = \sqrt{4\times 53} = 2\sqrt{53}$

$\bf\huge AC = \sqrt{(-2 - 1)^2 + ( - 11 - 5)^2}$

$\bf\huge AC = \sqrt{(-3)^2 + (- 16)^2}$

$\bf\huge AC = \sqrt{9 + 256} = \sqrt{265}$

$\bf\huge Hence \:A , B\: and \:C\: are\: not\: collinear$

$\bf\huge\boxed{\boxed{\:Regards=\:Yash\:Raj}}}$

Answer 2

Answer:

Step-by-step explanation:

As we have to assume that the points are collinear so the area of the triangle will be zero.

Then we can apply the formula to find the area of the triangle is equals to zero