Question

find the coordinates of the vertices of each figure after the given transformation.

1. rotation 180° about the origin

e(2, -2), j(1, 2), r(3, 3), s(5, 2)

1. reflection across y - axis

j(1, 3), u(0, 5), r(1, 5), c(3, 2)

1. translation: 7 units right and 1 unit down

j(-3, 1), f(-2, 3), n(-2, 0)

1. translation: 6 units right and 3 units down

s(-3, 3), c(-1, 4), w(-2, -1)

Explanation:

11. Rotation 180° about the origin

Step1: Recall rotation rule

The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$.

Step2: Apply rule to point E

For $E(2,-2)$, $x = 2,y=-2$. So $E'\to(-2,2)$.

Step3: Apply rule to point J

For $J(1,2)$, $x = 1,y = 2$. So $J'\to(-1,-2)$.

Step4: Apply rule to point R

For $R(3,3)$, $x = 3,y = 3$. So $R'\to(-3,-3)$.

Step5: Apply rule to point S

For $S(5,2)$, $x = 5,y = 2$. So $S'\to(-5,-2)$.

12. Reflection across y - axis

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the y - axis is $(x,y)\to(-x,y)$.

Step2: Apply rule to point J

For $J(1,3)$, $x = 1,y = 3$. So $J'\to(-1,3)$.

Step3: Apply rule to point U

For $U(0,5)$, $x = 0,y = 5$. So $U'\to(0,5)$.

Step4: Apply rule to point R

For $R(1,5)$, $x = 1,y = 5$. So $R'\to(-1,5)$.

Step5: Apply rule to point C

For $C(3,2)$, $x = 3,y = 2$. So $C'\to(-3,2)$.

13. Translation: 7 units right and 1 unit down

Step1: Recall translation rule

The rule for a translation of 7 units right and 1 unit down is $(x,y)\to(x + 7,y-1)$.

Step2: Apply rule to point J

For $J(-3,1)$, $x=-3,y = 1$. So $J'\to(-3 + 7,1-1)=(4,0)$.

Step3: Apply rule to point F

For $F(-2,3)$, $x=-2,y = 3$. So $F'\to(-2 + 7,3-1)=(5,2)$.

Step4: Apply rule to point N

For $N(-2,0)$, $x=-2,y = 0$. So $N'\to(-2 + 7,0-1)=(5,-1)$.

14. Translation: 6 units right and 3 units down

Answer:

$E'(- 2,2),J'(-1,-2),R'(-3,-3),S'(-5,-2)$