Straight Lines
Distance from Point to Line
Grade 11
Question:
<p>Consider a trapezoid ABCD, one of whose non parallel sides AB which is 8 cm long is perpendicular to the base. The base BC and AD of trapezoid are 6 cm and 10 cm in lengths respectively. Let \(L_1, L_2, L_3, L_4\) represent the lines AB, BC, CD and DA respectively and \(d(P, L)\) denote the perpendicular distance of point P from line L.</p><p>Find the area of region inside the trapezoid ABCD in which the point Q can lie satisfying \(d(Q, L_4) \leq d(Q, L_3)\):</p>
<p>(a) \(3(3\sqrt{5} + \sqrt{3})\)</p>
<p>(b) \(24(\sqrt{3} - 1)\)</p>
<p>(c) \(4(\sqrt{5} - \sqrt{5})\)</p>
<p>(d) \(25(\sqrt{5} - 1)\)</p>
Step-by-Step Solution
Key Concept: The locus of points equidistant from two lines forms an angle bisector. Find the region where distance to Lā (line AD) is less than or equal to distance to Lā (line CD).
<p>Not provided in source material.</p>
Correct Answer: A