If one diagonal of a square is along the line #x=2y# and one of its vertex is #(3,0)#, then its sides through the vertex are given by the equations?

Ans: #y-3x+9=0, x+3y-3=0#

1 Answer
CW
Dec 27, 2017

see explanation

Explanation:

enter image source here
As #A(3,0)# does not satisfy the diagonal #x=2y#,
#=> A(3,0)# does not lie on the diagonal #x=2y#.
Let #m# be the slope of a side passing through #A(3,0)#,
#=># equation of the side is : #y-0=m(x-3)#,
#=> y=m(x-3) ------color(red)(EQ1)#,
formula to find the angle between two lines :
#tantheta=|(m_1-m_2)/(1+m_1m_2)|#,
where #theta# is the angle between the two lines and #m_1 and m_2# are the slope of the two lines.
slope of the diagonal #x=2y# is #1/2#
#=> tan45=|(m-1/2)/(1+m*1/2)|#
#=> 1=|(m-1/2)/(1+m/2)|#
#=> m=3 or -1/3#
Substituting #m=3, and -1/3# in #color(red)(EQ1)#, we get :
#y=3(x-3), => color(red)(y-3x+9=0)#,
and,
#y=-1/3(x-3), => color(red)(3y+x-3=0)#

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