Question

7.) p(-3,8) q(7,5) r(2,3) s(-6,-1) reflect across x - axis
8.) p(5,3) q(1,-2) r(1,7) s(-2,0) reflect across y - axis
9.) p(4,2) q(2,4) r(2,-5) s(5,0) reflect across x = 2
10.) x(9,2) y(3,4) z(2,-2) reflect across x = 5
11.) x(-4,1) y(-2,0) z(-1,1) reflect across x - axis
12.) p(2,5) q(0,3) r(-2,5) s(0,-3) reflect across y = x

Explanation:

Step1: Recall reflection rules

• Reflection across x - axis: $(x,y)\to(x, - y)$
• Reflection across y - axis: $(x,y)\to(-x,y)$
• Reflection across $x = a$: $(x,y)\to(2a - x,y)$
• Reflection across $y=x$: $(x,y)\to(y,x)$

Step2: Solve 7.

• Reflect $P(-3,8)$ across x - axis: $P'(-3,-8)$
• Reflect $Q(7,5)$ across x - axis: $Q'(7,-5)$
• Reflect $R(2,3)$ across x - axis: $R'(2,-3)$
• Reflect $S(-6,-1)$ across x - axis: $S'(-6,1)$

Step3: Solve 8.

• Reflect $P(5,3)$ across y - axis: $P'(-5,3)$
• Reflect $Q(1,-2)$ across y - axis: $Q'(-1,-2)$
• Reflect $R(1,7)$ across y - axis: $R'(-1,7)$
• Reflect $S(-2,0)$ across y - axis: $S'(2,0)$

Step4: Solve 9.

• For point $P(4,2)$ reflected across $x = 2$, $x'=2\times2 - 4=0$, $y' = 2$, so $P'(0,2)$
• For point $Q(2,4)$ reflected across $x = 2$, $x'=2\times2 - 2=2$, $y' = 4$, so $Q'(2,4)$
• For point $R(2,-5)$ reflected across $x = 2$, $x'=2\times2 - 2=2$, $y'=-5$, so $R'(2,-5)$
• For point $S(5,0)$ reflected across $x = 2$, $x'=2\times2 - 5=-1$, $y' = 0$, so $S'(-1,0)$

Step5: Solve 10.

• For point $X(9,2)$ reflected across $x = 5$, $x'=2\times5 - 9 = 1$, $y'=2$, so $X'(1,2)$
• For point $Y(3,4)$ reflected across $x = 5$, $x'=2\times5 - 3=7$, $y' = 4$, so $Y'(7,4)$
• For point $Z(2,-2)$ reflected across $x = 5$, $x'=2\times5 - 2 = 8$, $y'=-2$, so $Z'(8,-2)$

Step6: Solve 11.

• Reflect $X(-4,1)$ across x - axis: $X'(-4,-1)$
• Reflect $Y(-2,0)$ across x - axis: $Y'(-2,0)$
• Reflect $Z(-1,1)$ across x - axis: $Z'(-1,-1)$

Step7: Solve 12.

• For point $P(2,5)$ reflected across $y = x$, $P'(5,2)$
• For point $Q(0,3)$ reflected across $y = x$, $Q'(3,0)$
• For point $R(-2,5)$ reflected across $y = x$, $R'(5,-2)$
• For point $S(0,-3)$ reflected across $y = x$, $S'(-3,0)$

Answer:

1. $P'(-3,-8),Q'(7,-5),R'(2,-3),S'(-6,1)$
2. $P'(-5,3),Q'(-1,-2),R'(-1,7),S'(2,0)$
3. $P'(0,2),Q'(2,4),R'(2,-5),S'(-1,0)$
4. $X'(1,2),Y'(7,4),Z'(8,-2)$
5. $X'(-4,-1),Y'(-2,0),Z'(-1,-1)$
6. $P'(5,2),Q'(3,0),R'(5,-2),S'(-3,0)$