If the points (x, 2), (5, – 2) and (8, 8) are collinear, find x using determinants.

Given: – (x, 2), (5, – 2) and (8, 8) are collinear points


Tip: – For Three points to be collinear, the area of the triangle formed by these points will be zero.


Now, we know that,


Vertices of a triangle are (x1,y1), (x2,y2) and (x3,y3), then the area of the triangle is given by:



Now,


Substituting given value in above formula




Expanding along R1



[x(– 6) + 2(– 3) + 1(24)] = 0


– 6x – 6 + 24 = 0


x = 3


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