<p>Find the possible coordinates of vertex A of a triangle with given sides, where the slope conditions and geometric constraints lead to specific coordinate values.</p>
Step-by-Step Solution
Key Concept: Use angle bisector properties to find diagonal directions, then solve the system to get vertex coordinates.
<p><strong>Step 1:</strong> The diagonal of the rhombus is parallel to the angle bisector of given lines.</p><p><strong>Step 2:</strong> Using the angle bisector formula: \(\frac{y - x - 2}{2} = \pm\frac{y - 7x - 3}{5\sqrt{2}}\)</p><p><strong>Step 3:</strong> This yields the diagonals: \(4y + 2x - 7 = 0\) and \(6y + 12x - 13 = 0\)</p><p><strong>Step 4:</strong> Solving the diagonal equations gives the diagonals as \(2y + x = 5\) and \(2x - y = 0\)</p><p><strong>Step 5:</strong> Therefore, possible coordinates of A are \((0, 5/2)\) or \((-5, -1)\)</p><p>∴ Answer is (b, c).</p>
Correct Answer: b, c