show that the points (2,-1),(3,0) and (4,1) are collinear.
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A(2,-1) , B(3,0) , C(4,1)
To show that ABC are collinear, show that C lies on line AB.
Step 1: Solve for the equation of AB.
I’ll use the Slope Intercept Form.
y = mx + b.
Solving for the slope, m = (0 +1) / (3 - 2 ) = ( 1/ 1) = 1
y = 1 (x) + b.
Knowing that this line hits A,
-1 = 1 ( 2 ) + b
-1 = 2+b
b = -3
Thus, line AB: y = 1 (x) - 3
Step 2: Substitute the x and y coordinates of C to check if it lies on the same line.
1 = 1(4)-3
1 = 4-3
1= 1
this is obviously true . Thus C lie on AB, and A,B,C are collinear.
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