<p>Two sides of a rhombus ABCD are parallel to lines \(y = x + 2\) and \(y = 7x + 3\). If the diagonals of the rhombus intersect at point \((1, 2)\) and the vertex A is on the y-axis, then the possible coordinates of A are:</p>
Step-by-Step Solution
Key Concept: Diagonals of a rhombus bisect each other at right angles, and opposite sides are parallel.
<p>In a rhombus, opposite sides are parallel, so one pair of opposite sides is parallel to \(y = x + 2\) and the other pair to \(y = 7x + 3\). The diagonals bisect each other at \((1, 2)\). Vertex A is on the y-axis, so \(A = (0, y_A)\). Using the property that diagonals bisect each other and the symmetry of the rhombus, we find \(A = \left(0, \frac{5}{2}\right)\) or \(A = (0, 5)\).</p>
Correct Answer: a, c