1.

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 (1, 2) and the vertex A is on the y-axis, then vertex A can be

Answer» y=x+2 slope=1
y=7x+3 slope=7
O(1,2)=`((0+m)/2,(n+alpha)/2)=((x+a)/2,(b+y)/2)`
m=2 x+a=2
`n+alpha=4 b+y=4`
`m_(ab)=(b-alpha)/(a-0)=1=b-alpha=a`
`m_(bc)=(b-n)/(a-2)=7=b-n=7(a-2)`
AB=BC
`sqrt((b-alpha)^2+(a-0)^2)=sqrt((b-n^2+(a-2)^2)`
solving this
`a=5/2,5/3`
`b=a+alpha=5/2+alpha,5/3+alpha`
`B(5/2,5/2+alpha),B(5/3,5/3+alpha)`
A(0,alpha) O(1,2)
`m_(OA)*m_(OB)=-1`
`(2-alpha)/(1-0)*((5/2)+alpha-2)/((5/2)-1)=-1`
solving this
`alpha=(0,3)`
A=`(0,alpha)`
A=(0,0),(0,3)


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