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# Find the value of x for which the points (x, – 1), (2,1) and (4, 5) are collinear.

Q : 8         Find the value of $x$ for which the points  $(x,-1),(2,1)$ and  $(4,5)$  are collinear.

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Point is collinear which means they lie on the same line by this we can say that their slopes are equal
Given points are A(x,-1) , B(2,1) and C(4,5)
$Slope = m = \frac{y_2-y_1}{x_2-x_1}$
Now,
The slope of AB = Slope of BC
$\frac{1+1}{2-x}= \frac{5-1}{4-2}$
$\frac{2}{2-x}= \frac{4}{2}\\ \\ \frac{2}{2-x} = 2\\ \\ 2=2(2-x)\\ 2=4-2x\\ -2x = -2\\ x = 1$
Therefore, the value of x is 1

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