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Point A is reflected over the line shown below to point B. Find the coordinates of B.
Write your answer as an ordered pair (x,y).
The line is y = x + 3, and A = (7,1).

 Jan 28, 2025
 #1
avatar+130383 
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The given line  has a slope of   1

 

A perpendicular line to  this  passing through  (7,1)  has the equation

 

y = - ( x -7) + 1

y = -x + 8

 

The x intersection of these two lines is

 

x + 3 =  -x + 8

2x = 5

x =5/2

And y = (5/2) + 3 =  11/2

 

From  (7,1)  to ( 5/2, 11/2)  we went  back to the left  7 -5/2  = 9/2  unirs

And  11/2 - 1  =  9/2  units up

 

So

 

B =  [ 5/2 - 9/2,  11/2 + 9/2]  =  ( -2, 10 )

 

 

cool cool cool

 Jan 28, 2025

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