Question

Chapter- COORDINATE GEOMETRY.
*Determine if the points(1,5)(2,3)and(-2,-11) are collinear*

Answer 1

if the area of the triangle, formed by these points, is zero,then the points are collinear

Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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