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Let B be the reflection of A over the line $y = \frac{1}{2} x + 2$.  Find the coordinates of B.

 

 May 5, 2022
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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)

 

 

cool cool cool

 May 5, 2022

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