Straight Lines
Optimization in Geometry
Grade 11
Question:
<p>Consider a trapezoid ABCD with AB = 8 cm perpendicular to the base, BC = 6 cm and AD = 10 cm. Distance of the point R lying on line AD from vertex A so that perimeter of triangle RBC is minimum is:</p>
<p>(a) 2</p>
<p>(b) 3</p>
<p>(c) 4</p>
<p>(d) 5</p>
Step-by-Step Solution
Key Concept: To minimize the perimeter of triangle RBC where R is on AD, use the reflection principle: reflect B across line AD to get B', then R is at the intersection of B'C with AD.
<p>Not provided in source material.</p>
Correct Answer: A