Points collinear

Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.

Result

x =  1

Solution:

BA=(x1;y1) CA=(x2,y2)  x1=3(1)=4 y1=23=1  x2=11(1)=12 y2=03=3  k1=x2/x1=12/4=3 k2=y2/y1=(3)/(1)=3  k1=k2   3 (4;1)=(12;3) 3 BA=CA x=1BA=(x_{1};y_{1}) \ \\ CA=(x_{2},y_{2}) \ \\ \ \\ x_{1}=3 - (-1)=4 \ \\ y_{1}=2-3=-1 \ \\ \ \\ x_{2}=11 - (-1)=12 \ \\ y_{2}=0 - 3=-3 \ \\ \ \\ k_{1}=x_{2}/x_{1}=12/4=3 \ \\ k_{2}=y_{2}/y_{1}=(-3)/(-1)=3 \ \\ \ \\ k_{1}=k_{2} \ \\ \ \\ \ \\ 3 \cdot \ (4;-1)=(12; 3) \ \\ 3 \cdot \ BA=CA \ \\ x=1



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For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
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