Question

Verify that the points (1,5) (2,3) (-2,-1) are collinear or points

Answer 1

Answer:

Consider that, if all the points are collinear then the longest distance must be the sum of the smaller distances.

Step-by-step explanation:  

Take the points as follows:

( 1 , 5 ) → A

( 2 , 3 ) → B

( -2 , -1 ) → C

Now let's find the distances of all the three possible points namely:

AB, BC, AC

Recall that the distance formula is given by D = $\sqrt{ ( x2 - x1 )^{2} + ( y2 - y 1 )^{2}$

Now: AB = $\sqrt{( 2 - 1 )^{2} + ( 3 - 5 )^{2} }$ = $\sqrt{( 1 ) + ( 4 ) }$ = $\sqrt{5}$

Similarly  BC = $\sqrt{32\\}$  and AC = $\sqrt{45}$  

Now  clearly AC is the longest line therefore BC + AB should equal AC in order for the lines to be collinear or else the lines are not collinear.

Now let's simplify: BC + AB =  $\sqrt{32\\}$  + $\sqrt{5}$  = 7.892

But AC = $\sqrt{45}$  = 6.708

Thus AC ≠ BC + AB and the line is not collinear.