Question 11

# ABCD is a parallelogram whose diagonals are parallel to the lines $$2y—x—5=0$$ and $$y+2x—7=0$$ respectively.Then ABCDis -

Solution

The slope of any line parallel to 2y - x - 5 = 0 would be 1/2
The slope of any line parallel to y + 2x - 7 = 0 would be -2

Product of slopes = -1 which shows that these 2 lines would be perpendicular i.e. we have a parallelogram whose diagonals are perpendicular to each other. This means that the quadrilateral is atleast a rhombus and it would be a square if we can get info that all sides are equal to each other.