Question

Which set of points correctly demonstrates a pre-image that has been is reflected over x = -1? A(0,-1) and A'(4,-1) A(0,-5) and A'(0,3) A(-5,0) and A'(3,0) A(0,-4) and A'(0,4)

Answer 1

Points reflected across x = -1 will be the same distance from it but on the opposite side. The y-values will stay the same for the reflected point. So you can cross out the 2nd and 4th options because they have different y-values. That leaves us with the 1st and 3rd options:

A(0, -1) and A'(4, -1)

See if the x-values are the same distance from -1.

|0 - (-1)| = 1
|4 - (-1)| = 5

The distances are different so let's try the other one:

A(-5, 0) and A'(3, 0)

See if the x-values are the same distance from -1.

|-5 - (-1)| = 4
|3 - (-1)| = 4

The distances are the same, so these points correctly demonstrate a pre-image that has been reflected over x = -1.