Question 698900
You have to use the formula for distance between 
two points. One of the points in every case is (0,0)
( the origin ). 
distance formula:
{{{ d = sqrt( ( x[2] - x[1] )^2 + ( y[2] - y[1] )^2 ) }}}
(A)
( x2, y2 ) = (0, -7)
{{{ d = sqrt( ( 0 - 0 )^2 + ( -7 - 0 )^2 ) }}}
{{{ d = sqrt( -7 )^2 }}}
{{{ d = 7 }}}
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(B)
( -3,8 )
{{{ d = sqrt( ( -3 - 0 )^2 + ( 8 - 0 )^2 ) }}}
{{{ d = sqrt( (-3)^2 + 8^2 ) }}}
{{{ d = sqrt( 9 + 64 ) }}}
{{{ d = sqrt( 73 ) }}}
{{{ d = 8.544 }}}
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(C)
(-4,-3)
{{{ d = sqrt( ( -4 - 0 )^2 + ( -3 - 0 )^2 ) }}}
{{{ d = sqrt( (-4)^2 + (-3)^2 ) }}}
{{{ d = sqrt( 16 + 9 ) }}}
{{{ d = sqrt( 25 ) }}}
{{{ d = 5 }}}
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(D)
(5,1)
{{{ d = sqrt( ( 5 - 0 )^2 + ( 1 - 0 )^2 ) }}}
{{{ d = sqrt( 5^2 + 1^2 ) }}}
{{{ d = sqrt( 25 + 1 ) }}}
{{{ d = sqrt( 26 ) }}}
{{{ d = 5.099 }}}
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(B) (-3,8) lies farthest from the origin