Give the coordinates of the points after a reflection over the line y=-4

Question

Give the coordinates of the points after a reflection over the line y=-4

 

A( 4,5) A' (_,_)

B(0,4) B' (_,_)

C(-2,1) C' (_,_)


use algebraic representation and please show your work

Answer 1

The line y = -4 is horizontal.  

 

If a point is reflected over a horizontal line, the x-coordinate is unchanged.  

 

The point (4,5) lies 9 units above the line y = -4, so (4,5) is reflected to the point that has x-coordinate 4 and y-coordinate that is 9 units below the line y = -4, namely (4, -13).  

 

Similarly, for B(0,4), B'(0,-12) and for C(-2,1), C'(-2, -9).