Question

Verify whether following points (1,-1) (4,1) and (-2, -3) are collinear or
not?
​

Answer 1

Answer:

Step-by-step explanation:

( $x_{1}$ , $y_{1}$ )

( $x_{2}$ , $y_{2}$ )

m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

y - $y_{1}$ = m( x - $x_{1}$ )

~~~~~~~~~~~~~~~~~

( 4 , 1 )

( - 2 , - 3 )

m = $\frac{-3-1}{-2-4}$ = $\frac{-4}{-6}$ = $\frac{2}{3}$

y - 1 = $\frac{2}{3}$ ( x - 4)

y = $\frac{2}{3}$ x - $\frac{5}{3}$

( 1 , - 1 ) → y = $\frac{2}{3}$ x - $\frac{5}{3}$

- 1 = $\frac{2}{3}$ ( 1 ) - $\frac{5}{3}$

- 1 = - 1 ⇒ three given points are collinear.