Question

1. reflection across the y-axis

$z(0, 0), y(0, 4), x(3, 4), w(4, -1)$

1. reflection across the y-axis

$j(-3, 4), k(-2, 5), l(-2, 4)$

1. reflection across the y-axis

$k(2, -5), l(1, 0), m(3, -1)$

1. reflection across the y-axis

$d(1, -4), c(0, -3), b(3, -2), a(5, -3)$

1. rotation $180^{\circ}$ about the origin

$f(1, -1), g(0, 4), h(5, 3), i(2, -2)$

1. rotation $90^{\circ}$ counterclockwise about the origin

$p(-2, 2), q(-1, 4), r(3, 3)$

1. rotation $180^{\circ}$ about the origin

$k(-5, 2), l(-5, 5), m(-3, 2)$

1. rotation $180^{\circ}$ about the origin

$h(1, 3), g(2, 5), f(3, 1)$

1. rotation $180^{\circ}$ about the origin

$l(-5, -2), k(-4, -2), j(-3, -4)$

Explanation:

Step1: Reflect over y-axis: $(x,y)\to(-x,y)$

$Z(0,0)\to Z'(0,0),\ Y(0,4)\to Y'(0,4),\ X(3,4)\to X'(-3,4),\ W(4,-1)\to W'(-4,-1)$

Step2: Reflect over y-axis: $(x,y)\to(-x,y)$

$J(-3,4)\to J'(3,4),\ K(-2,5)\to K'(2,5),\ L(-2,4)\to L'(2,4)$

Step3: Reflect over y-axis: $(x,y)\to(-x,y)$

$K(2,-5)\to K'(-2,-5),\ L(1,0)\to L'(-1,0),\ M(3,-1)\to M'(-3,-1)$

Step4: Reflect over y-axis: $(x,y)\to(-x,y)$

$D(1,-4)\to D'(-1,-4),\ C(0,-3)\to C'(0,-3),\ B(3,-2)\to B'(-3,-2),\ A(5,-3)\to A'(-5,-3)$

Step5: Rotate $180^\circ$: $(x,y)\to(-x,-y)$

$F(1,-1)\to F'(-1,1),\ G(0,4)\to G'(0,-4),\ H(5,3)\to H'(-5,-3),\ I(2,-2)\to I'(-2,2)$

Step6: Rotate $90^\circ$ counterclockwise: $(x,y)\to(-y,x)$

$P(-2,2)\to P'(-2,-2),\ Q(-1,4)\to Q'(-4,-1),\ R(3,3)\to R'(-3,3)$

Step7: Rotate $180^\circ$: $(x,y)\to(-x,-y)$

$K(-5,2)\to K'(5,-2),\ L(-5,5)\to L'(5,-5),\ M(-3,2)\to M'(3,-2)$

Step8: Rotate $180^\circ$: $(x,y)\to(-x,-y)$

$H(1,3)\to H'(-1,-3),\ G(2,5)\to G'(-2,-5),\ F(3,1)\to F'(-3,-1)$

Step9: Rotate $180^\circ$: $(x,y)\to(-x,-y)$

$L(-5,-2)\to L'(5,2),\ K(-4,-2)\to K'(4,2),\ J(-3,-4)\to J'(3,4)$

Answer:

1. $Z'(0,0),\ Y'(0,4),\ X'(-3,4),\ W'(-4,-1)$
2. $J'(3,4),\ K'(2,5),\ L'(2,4)$
3. $K'(-2,-5),\ L'(-1,0),\ M'(-3,-1)$
4. $D'(-1,-4),\ C'(0,-3),\ B'(-3,-2),\ A'(-5,-3)$
5. $F'(-1,1),\ G'(0,-4),\ H'(-5,-3),\ I'(-2,2)$
6. $P'(-2,-2),\ Q'(-4,-1),\ R'(-3,3)$
7. $K'(5,-2),\ L'(5,-5),\ M'(3,-2)$
8. $H'(-1,-3),\ G'(-2,-5),\ F'(-3,-1)$
9. $L'(5,2),\ K'(4,2),\ J'(3,4)$