Straight Lines
Transformations and Distance
Grade 11
Question:
<p>If <span class="math">C</span> is the reflection of <span class="math">A(2, 4)</span> in X-axis and <span class="math">B</span> is the reflection of <span class="math">C</span> in Y-axis, then <span class="math">|AB|</span> is equal to</p>
<p>(a) 20</p>
<p>(b) <span class="math">2\sqrt{5}</span></p>
<p>(c) <span class="math">4\sqrt{5}</span></p>
<p>(d) 4</p>
Step-by-Step Solution
Key Concept: Apply reflection formulas: reflection in X-axis changes sign of y-coordinate; reflection in Y-axis changes sign of x-coordinate. Then use the distance formula.
<p><strong>Step 1:</strong> Reflection of <span class="math">A(2, 4)</span> in the X-axis gives <span class="math">C(2, -4)</span></p><p><strong>Step 2:</strong> Reflection of <span class="math">C(2, -4)</span> in the Y-axis gives <span class="math">B(-2, -4)</span></p><p><strong>Step 3:</strong> Distance <span class="math">|AB| = \sqrt{(2-(-2))^2 + (4-(-4))^2} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}</span></p><p>∴ Answer is C.</p>
Correct Answer: c