Vector mains 2018 Q 11 The sides of a rhombus ABCD are parallel to the lines, x - y - Maths - Vector Algebra

Question

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

Neha Sethi · Accepted Answer

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 -12⇒a-20-1=2 or a-20-1=-12⇒a=0 or a=52Hence ordinate of point A is 52 or 0
Regards

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