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Let \(A = (6,2)\), and let \(B\) be the reflection of \(A\) over the line \(y = \frac{1}{2} x + 5\). Find the coordinates of \(B\).

 

(No image was given for this problem)

 

(The answer is not (12/5,51/5) I tried solving it and got that answer, but it was incorrect.)

 

Thank you very much!

 May 3, 2020
 #1
avatar+111326 
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Here's one way to do this

 

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

 

And the equation of a line with this slope  passing  through A  has the form

 

y  = -2 (x - 6) + 2

 

y = -2x + 12 + 2

 

y = -2x + 14

 

Lets  find  the x intersection of  these two lines

 

(1/2)x + 5  =  -2x + 14          add 2x   subtract 5

 

(5/2)x  =  9     multiply  both sides by 2/5

 

x = (18/5) =  3.6

 

And y  = -2(18/5) + 14  =  -36/5 + 14 =  (34/5) =  6.8

 

So  to  find  B  we  can do this

 

( 3.6  - ( 6 - 3.6)  , 6.8 - ( 2 - 6.8) )  =  ( 3.6 - 2.4, 6.8 - (-4.8) )  =  ( 1.2, 11.6)

 

Here's a pic :

 

 

 

cool cool cool

 May 3, 2020

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