Straight Lines
Parallelogram properties
Grade 11
Question:
<p>Vertices of a parallelogram <span class="math inline">\(ABCD\)</span> are <span class="math inline">\(A(3, 1)\)</span>, <span class="math inline">\(B(13, 6)\)</span>, <span class="math inline">\(C(13, 21)\)</span> and <span class="math inline">\(D(3, 16)\)</span>. If a line passing through the origin divides the parallelogram into two congruent parts then the slope of the line is:</p>
<p>(a) <span class="math inline">\(\frac{11}{12}\)</span></p>
<p>(b) <span class="math inline">\(\frac{11}{8}\)</span></p>
<p>(c) <span class="math inline">\(\frac{25}{8}\)</span></p>
<p>(d) <span class="math inline">\(\frac{13}{8}\)</span></p>
Step-by-Step Solution
Key Concept: A line dividing a parallelogram into two congruent parts must pass through the center (intersection of diagonals) of the parallelogram.
<p><strong>Solution:</strong> A line dividing a parallelogram into two congruent parts must pass through the center of the parallelogram. The center is the midpoint of the diagonals. Center <span class="math inline">\(= \left(\frac{3+13}{2}, \frac{1+21}{2}\right) = (8, 11)\)</span>. The line passes through the origin <span class="math inline">\((0, 0)\)</span> and the center <span class="math inline">\((8, 11)\)</span>. Slope <span class="math inline">\(= \frac{11 - 0}{8 - 0} = \frac{11}{8}\)</span>.</p>
Correct Answer: B