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Mirror image of a point in a line with unknowns in the point or the image: find them

The same question, asked 3 times: 2021 Paper 2*, 22 Jan 2026 S1*, 4 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 2

    61
    Let a,b∈Ra,b\in R. If the mirror image of the point P(a,6,9)P(a,6,9) with respect to the line x−37=y−25=z−1−9\frac{x- 3}{7}=\frac{y- 2}{5}=\frac{z- 1}{- 9} is (20,b,−a−9)(20,b, -a- 9), then ∣a+b∣|a+b| is equal to:

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  2. Question 2

    22 Jan 2026 S1

    61
    If the image of the point P(1,2,a)P(1,2,a) in the line x−63=y−72=7−z2\frac{x - 6}{3}=\frac{y - 7}{2}=\frac{7 - z}{2} is Q(5, b,c)Q(5,\text{ }b,c), then a2+b2+c2a^{2}+b^{2}+c^{2} is equal to

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  3. Question 3

    4 Apr 2026 S2

    64
    If (2α+1,α2−3α,α−12)\left( 2\alpha+ 1,\alpha^{2}- 3\alpha,\frac{\alpha- 1}{2} \right) is the image of (α,2α,1)(\alpha,2\alpha,1) in the line x−23=y−12=z1\frac{x - 2}{3}=\frac{y - 1}{2}=\frac{z}{1}, then the possible value(s) of α\alpha is(are) :

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