Question

Two sides of a rhombus ABCD are parallel to the lines y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at the point and the vertex A is on the y-axis, Find possible coordinates of A.

Answer 1

Let the coordinates of A be (0, α). Since, the sides AB and AD are parallel to the lines y = x + 2 and y = 7x + 3 respectively.

.'. The diagonal AC is parallel to the bisector of the angle between these two lines. The equation of the bisectors are given by

Thus, the diagonals of the rhombus are parallel to the lines 2x + 4 y - 7 = 0 and 12 - 6y + 13 = 0.

Hence, the coordinates are (0, 5/ 2) or (0, 0).