Question

D(-2,-3), E(1,0), F(2,1) Determine whether the given points are collinear or not.

Answer 1

Answer - Yes. 

Explanation -

Let the Points D(-2,3), E(1,0), N(2,1) be D(x₁, y₁), E(x₂,y₂), F(x₃,y₃).

Let us first find the Slope of DE,

∵ m = $\frac{y_2 - y_1}{x_2 - x_1}$
∴ m = (0 + 3)/(1 + 2)    
        = 3/3 
        = 1

Now For th Slope of EF, 

m = $\frac{y_3 - y_2}{x_3 - x_2}$   
    = (1 - 0)/(2 - 1)  
    = 1  

Since, the Slope of both the lines DE and EF are same therefore, Points are Collinear.


Hope it helps.

Answer 2

SOLUTION:-
GIVEN BY POINT :-
D(-2 , -3) , E( 1 , 0) , F( 2 , 1)

if DE + EF = DF
then given point is collinear

DE =
$= \sqrt{ {(1 + 2)}^{2} + {(0 + 3)}^{2} } \\ = \sqrt{9 + 9} = \sqrt{18} = 3 \sqrt{2}$
DF =
$= \sqrt{ {(2 + 2)}^{2} + {( 1+ 3)}^{2} } \\ = \sqrt{ 16 + 16 } = \sqrt{32} = 4 \sqrt{2}$
EF =
$= \sqrt{ {(2 - 1)}^{2} + {(1 - 0)}^{2} } \\ = \sqrt{ {1}^{2} + {( 1)}^{2} } \\ = \sqrt{1 + 1} = \sqrt{2}$
now ,
=>DE + EF = DF
=>
$3 \sqrt{2} + \sqrt{2} = 4 \sqrt{2} \\ 4 \sqrt{2} = 4 \sqrt{2}$

●the givens points are collinear●


■I HOPE ITS HELP■