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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 8 of 74
Marks: +1, -0
Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
Solution:  
Let A(x, –1), B(2, 1) and C(4, 5) be the given collinear points. Then by collinearity of A, B, C, we have slope of AB = slope of BC
⇒ 1−(−1)2−x\frac{1-(-1)}{2-x} = 5−14−2\frac{5-1}{4-2} ⇒ 22−x\frac{2}{2-x} = 2
⇒ 2 – x = 1 ⇒ x = 1
Hence for x = 1, A, B & C are collinear.
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