Straight Lines
Slope of a line
Grade 11
Question:
<p>Vertices of a parallelogram <em>ABCD</em> are A(3, 1), B(13, 6), C(13, 21) and D(3, 16). If a line passing through the origin divides the parallelogram into two congruent parts, then the slope of the line is</p>
<p>(a) 11/12</p>
<p>(b) 11/8</p>
<p>(c) 25/8</p>
<p>(d) 13/8</p>
Step-by-Step Solution
Key Concept: A line divides a parallelogram into two congruent parts if and only if it passes through the center (intersection point of diagonals). The center of a parallelogram is the midpoint of both diagonals.
<p><strong>Step 1:</strong> Find the center of parallelogram ABCD by finding the midpoint of diagonal AC (or BD).</p><p>Center = Midpoint of AC = ((3+13)/2, (1+21)/2) = (8, 11)</p><p><strong>Step 2:</strong> Verify using diagonal BD: Midpoint of BD = ((13+3)/2, (6+16)/2) = (8, 11) ✓</p><p><strong>Step 3:</strong> The line passes through origin O(0, 0) and center P(8, 11).</p><p><strong>Step 4:</strong> Calculate the slope of line OP:</p><p>m = (11 - 0)/(8 - 0) = 11/8</p><p>∴ Answer: A (slope = 11/8)</p>
Correct Answer: A