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  4. If the points ( x, y), (1, 2) and ( -3, 4) are collinear, then

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Q. If the points ( x, y), (1, 2) and ( -3, 4) are collinear, then

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Solution:

If (x, y), (1, 2) and (-3, 4) are collinear then slope of line joining (x, 4) and (1, 2) is same as line joining points (1, 2) and ( -3, 4) or line joining (x, 4) to (- 3, 4).
$So, \frac{2-y}{1-x} = \frac{4-2}{-3-1} = \frac{4-y}{-3-x} \Rightarrow \frac{2-y}{1-x} =- \frac{1}{2} $
$ \Rightarrow \frac{y-2}{1-x} = \frac{1}{2} \Rightarrow -4 + 2y = 1 -x \Rightarrow x +2y -5 = 0 $