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