Question

Determine if the points (1,5) , (2,3) , (-2,-11) are collinear then find AB, BC, CA

Answer 1

Answer:

$AB=\sqrt{5}$,$BC=15$ , $CA=\sqrt{262}$

Step-by-step explanation:

|--------------------|---------------|

A                     B               C

(1,5)                (2,3)           (-2,-11)

here,        

 $x_1=1\\x_2=2\\x_3=-2$        $y_1=5\\y_2=3\\y_3=-11$

Distance formula  

$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

$AB=\sqrt{1+4} \\\\AB=\sqrt{5}$

$BC=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}$

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

$BC=\sqrt{225} =15$

$CA=\sqrt{(x_3-x_1)^2+(y_3-y_1)^2} \\\\CA=\sqrt{(-2-1)^2+(-11-5)^2} \\\\CA=\sqrt{6+256} \\\\CA=\sqrt{262}$