The point A(5,6) is reflected about the line x = 1, then about the line x = k. The final image is A”(11,6). What is the value of k? A.) -4 B.) 4 C.) 1 D.) 11

Question

The point A(5,6) is reflected about the line x = 1, then about the line x = k. The final image is A”(11,6). What is the value of k?

A.) -4

B.) 4

C.) 1

D.) 11

 

I'm a bit confused as to what this is asking me. I know the line lies on 1 and the point A is on 5,6 but when I reflect it I get confused.

Answer 1

The point (5,6) is 4 units to the right of the vertical line x=1,  The reflected point will be on the same horizontal line as (5,6) and will be 4 units to the left of the line of reflection, x=1.  So, the reflected point is (-3,6).

 

If (-3,6) is then reflected through x=k so that the reflected point is (11,6), the point (k,6) would be on the horizontal line through (-3,6) and (11,6) and is halfway between (-3,6) and (11,6).  

 

So, (k,6) = (4,6).  Therefore, k = 4. (Answer B)