Question

R(0,3), D(2,1), S(3,-1) Determine whether the points are collinear.

Answer 1

Answer - No. 

Explanation -

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

Let us first find the Slope of RS,

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

Now For th Slope of DS, 

m = $\frac{y_3 - y_2}{x_3 - x_2}$   
    = (-1 - 1)/(3 - 2)  
    = -2/1
    = -2 

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


Hope it helps.

Answer 2

Let R(0,3)=(x1,y1), D(2,1)=(x2,y2)

And S(3,-1)=(x3,y3) ,

Area∆RDS

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

=1/2|0[1-(-1)]+2[-1-3]+3[3-1]|

= 1/2| 0 + 2(-4) + 3 × 2 |

= 1/2 | -8 + 6 |

= 1/2 | -2 |

= 2/2

= 1

Therefore ,

∆RDS ≠ 0

R , D and S are not collinear.

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