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Question
Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear ?
Solution
The points (x1, y1), (x2, y2) and (x3, y3) are collinear if `x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)`= 0 i.e., the area of triangle formed by the given points is zero.
Let the given points be A (x, − 1), B (2, 1) and C (4, 5).
The points A (x, − 1), B (2, 1) and C (4, 5) are collinear.
Therefore, Area of ΔABC = 0
`rArrx(1-5)+2[5-(-1)]+4(-1-1)=0`
`rArrx-4x+12-8=0`
`rArrx-4x+4=0`
`rArrx=1`
Thus, the value of x is 1.
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