Vector mains 2018
Q.11. The sides of a rhombus ABCD are parallel to the lines, x - y + 2 = 0 and 7x - y + 3 = 0. If the diagonals of the rhombus intersect at P (1, 2) and the vertex A (different from the origin) is on the y-axis, then the ordinate of A is :
1. 2
2. 7 2
3. 5 2
4. 7 4

Dear student
Given the coordinates of P as 1,2Let the coordinates of the vertex A be 0,a.As the sides of the rhombusare parallel to the lines y=x+2 and y=7x+3 ,its diagonals are parallel to the  bisectors of the angles between these lines,i.e. y-x-21+1=±y-7x-31+49i.e. y-x-22=±y-7x-352i.e y-x-2=±y-7x-35i.e 5y-5x-10=±y-7x-3i.e 5y-5x-10=y-7x-3 or 5y-5x-10=-y-7x-35y-5x-10=y-7x-3 or 5y-5x-10=-y+7x+32x+4y-7=0 or 12x-6y+13=0Therefore, the slope of AO is 2 or -12a-20-1=2 or a-20-1=-12a=0 or a=52Hence ordinate of point A is 52 or 0.

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