+0

0
52
1

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
+111326
+1

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 :

May 3, 2020