Answer:
A. (x + 1, y − 4), reflection over y = x − 4
Step-by-step explanation:
You must perform all the composed transformations to spot the one in which the coordinates of the preimage and the image are not the same.
The coordinates of the preimage are A(0,1), B(3,4), C(5,2) , and D(2,-1)
Option A is a translation (x + 1, y − 4), followed by a reflection over y = x − 4.
[tex]A(0,1)\to(1,-3)\to A'(1,-3)[/tex]
[tex]B(3,4)\to(4,0)\to B'(4,0)[/tex]
[tex]C(5,2)\to(6,-2)\to C'(2,2)[/tex]
[tex]D(2,-1)\to(3,-5)\to D'(-1,-1)[/tex]
Option B is a translation (x − 4, y − 4), followed by a reflection over y = −x
[tex]A(0,1)\to(-4,-3)\to A'(0,1)[/tex]
[tex]B(3,4)\to(-1,0)\to B'(3,4)[/tex]
[tex]C(5,2)\to(1,-2)\to C'(5,2)[/tex]
[tex]D(2,-1)\to(-2,-5)\to D'(2,-1)[/tex]
Option C is a translation (x +3, y − 3), followed by a reflection over y = x-4
[tex]A(0,1)\to(3,-2)\to A'(0,1)[/tex]
[tex]B(3,4)\to(6,1)\to B'(3,4)[/tex]
[tex]C(5,2)\to(8,-1)\to C'(5,2)[/tex]
[tex]D(2,-1)\to(5,-4)\to D'(2,-1)[/tex]
Option D is a translation (x +4, y + 4), followed by a reflection over y = −x+8
[tex]A(0,1)\to(4,5)\to A'(0,1)[/tex]
[tex]B(3,4)\to(7,8)\to B'(3,4)[/tex]
[tex]C(5,2)\to(9,6)\to C'(5,2)[/tex]
[tex]D(2,-1)\to(6,3)\to D'(2,-1)[/tex]
The correct choice is A.
