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The slope of  the line perpendicular to the given line  is   -2

A line with this slope going through A  has the equation

y  = -2 ( x -3) + 1

y = -2x + 7

Setting the two equations   equal  to  find the x intersection of  these lines we have

(1/2)x + 2 =  -2x + 7

(5/2)x  =  5

x =  5 ( 2/5)   = 2

And the y intersection = -2(2) + 7   =   3

So the intersection pt  is (2,3)

Using the midpoint rule we can find the coordinates of B as

[ 3 + x] / 2 = 2   ⇒    3+ x = 4   ⇒    x  =1

[1 + y] / 2  =  3   ⇒ 1 + y = 6 ⇒   y =  5

So

B = ( 1 , 5)