Question

What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?

'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at negative 4, negative 2, B double prime at negative 4, negative 1, C double prime at negative 1, negative 1, D double prime at negative 1, negative 2.

Answer 1

original diagram:


choices:
Reflected over the x-axis and rotated 180°
Reflected over the y-axis and rotated 180°
Reflected over the x-axis and rotated 90° counterclockwise
Reflected over the y-axis and rotated 90° counterclockwise

Answer 2

thoughts?

can you try going through each of the choices and seeing if it takes you from ABCD to A'B'C'D?

for example, let's look at the first choice

Reflected over the x-axis and rotated 180°

let's see what happens when we apply this:

first, we'll reflect over the x-axis. the x-coordinates stay the same, but the y-coordinates get multiplied by -1 to produce the image.

Answer 3

however, we're not done yet. notice how the first answer choice also says "rotated 180°"

applying the180 degree rotation, every coordinate in the blue rectangle gets multiplied by -1. thinking about this visually, it should end up in quadrant II, and therefore does *not* coincide with the image A'B'C'D, and therefore, choice 1 is not the solution



repeat this logic with the three other answer choices until you find the one that produces the afterimage A'B'C'D' given in the problem

let me know if you're still confused, or want to check your solution