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!
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 :