Question

L(-2,3), M(1,-3), N(5,4) Determine whether the points are collinear.

Answer 1

Answer - No. 

Explanation -

Let the Points L(-2,3), M(1,-3), N(5,4) be L(x₁, y₁), M(x₂,y₂), N(x₃,y₃).

Let us first find the Slope of LM,

∵ m = $\frac{y_2 - y_1}{x_2 - x_1}$
∴ m = (-3 - 3)/(1 - 3)   
        = -6/-2  
        = 3

Now For th Slope of MN, 

m = $\frac{y_3 - y_2}{x_3 - x_2}$   
    = (4 + 3)/(5 - 1) 
    = 7/4  

Since, the Slope of both the lines LM, and MN are not same therefore, Points are non-Collinear.


Hope it helps.

Answer 2

Let L(-2,3) = ( x1,y1) , M(1,-3)=(x2,y2)

N(5,4)=(x3,y3) are three points .

Area∆LMN

=1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

=1/2|(-2)[-3-4]+1[4-3]+5[3+3]|

=1/2|(-2)(-7)+1+5×6|

= 1/2| 14 + 1 + 30 |

= 1/2 | 45 |

Therefore ,

Area of ∆LMN ≠ 0

L , M and N are not collinear.

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