<p>The image of the point A(1, 2) by the line mirror \(y = x\) is the point B and the image of B by the line mirror \(y = 0\) is the point \((\alpha, \beta)\). Then</p>
<p>A. \(\alpha = 1,\ \beta = -2\)</p>
<p>B. \(\alpha = 0,\ \beta = 0\)</p>
<p>C. \(\alpha = 2,\ \beta = -1\)</p>
<p>D. none of these</p>
Step-by-Step Solution
Key Concept: Reflection across y = x swaps coordinates (x, y) → (y, x), then reflection across y = 0 (x-axis) negates the y-coordinate (x, y) → (x, -y). Apply these transformations sequentially.
<p><strong>Step 1:</strong> Reflect A(1, 2) across the line mirror y = x.</p><p>When reflecting across y = x, we swap coordinates: (x, y) → (y, x)</p><p>So A(1, 2) → B(2, 1)</p><p><strong>Step 2:</strong> Reflect B(2, 1) across the line mirror y = 0 (the x-axis).</p><p>When reflecting across y = 0, the x-coordinate stays the same and y-coordinate becomes its negative: (x, y) → (x, -y)</p><p>So B(2, 1) → (2, -1)</p><p><strong>Step 3:</strong> Compare with (α, β).</p><p>Therefore: α = 2 and β = -1</p><p>∴ Answer: C</p>
Correct Answer: C