Question

1. reflect over the x - axis

pre - image image
a(4,1) a(\t,\t)
b(2, - 1) b(\t,\t)
c(2, - 4) c(\t,\t)
d(4, - 4) d(\t,\t)
rule: (x,y)→(\t,\t)

1. (x,y)→( - x,y)

pre - image image
a(0,3) a(\t,\t)
b(6,5) b(\t,\t)
c(2,5) c(\t,\t)
description:

1. (x,y)→(x, - y)

pre - image image
a(0,0) a(\t,\t)
b(1, - 2) b(\t,\t)
c( - 4, - 1) c(\t,\t)
d( - 3, - 3) d(\t,\t)
description:

Explanation:

8.

Step1: Recall reflection rule over x - axis

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

Step2: Apply rule to point A

For $A(4,1)$, using the rule $(x,y)\to(x, - y)$, we get $A'(4,-1)$.

Step3: Apply rule to point B

For $B(2,-1)$, using the rule $(x,y)\to(x, - y)$, we get $B'(2,1)$.

Step4: Apply rule to point C

For $C(2,-4)$, using the rule $(x,y)\to(x, - y)$, we get $C'(2,4)$.

Step5: Apply rule to point D

For $D(4,-4)$, using the rule $(x,y)\to(x, - y)$, we get $D'(4,4)$.

Step1: Recall the given transformation rule

The rule is $(x,y)\to(-x,y)$. This represents a reflection over the y - axis.

Step2: Apply rule to point A

For $A(0,3)$, using the rule $(x,y)\to(-x,y)$, we get $A'(0,3)$ (since $-0 = 0$).

Step3: Apply rule to point B

For $B(6,5)$, using the rule $(x,y)\to(-x,y)$, we get $B'(-6,5)$.

Step4: Apply rule to point C

For $C(2,5)$, using the rule $(x,y)\to(-x,y)$, we get $C'(-2,5)$.

Step1: Recall the given transformation rule

The rule $(x,y)\to(x,-y)$ represents a reflection over the x - axis.

Step2: Apply rule to point A

For $A(0,0)$, using the rule $(x,y)\to(x,-y)$, we get $A'(0,0)$ (since $-0 = 0$).

Step3: Apply rule to point B

For $B(1,-2)$, using the rule $(x,y)\to(x,-y)$, we get $B'(1,2)$.

Step4: Apply rule to point C

For $C(-4,-1)$, using the rule $(x,y)\to(x,-y)$, we get $C'(-4,1)$.

Step5: Apply rule to point D

For $D(-3,-3)$, using the rule $(x,y)\to(x,-y)$, we get $D'(-3,3)$.

Answer:

Pre - Image	Image
$B(2,-1)$	$B'(2,1)$
$C(2,-4)$	$C'(2,4)$
$D(4,-4)$	$D'(4,4)$

Rule: $(x,y)\to(x, - y)$

9.