Question

plot and connect the pre - image points listed in the table. reflect each shape as specified, list the new image coordinates, and rewrite the description as a rule or the rule as a description.

1. reflect over the x - axis

pre - image	image
b(4,1)	b(, )
c(2,5)	c(, )

rule: (x,y)→(, )

1. reflect over the y - axis

pre - image	image
b(-6,3)	b(, )
c(-4,6)	c(, )
d(-2,3)	d(, )

rule: (x,y)→(, )

Explanation:

Step1: Recall reflection over x - axis rule

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

Step3: Apply rule to point B

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

Step4: Apply rule to point C

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

Step5: Recall reflection over y - axis rule

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

Step6: Apply rule to point A

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

Step7: Apply rule to point B

For point $B(-6,3)$, using the rule $(x,y)\to(-x,y)$, we get $B'(6,3)$.

Step8: Apply rule to point C

For point $C(-4,6)$, using the rule $(x,y)\to(-x,y)$, we get $C'(4,6)$.

Step9: Apply rule to point D

For point $D(-2,3)$, using the rule $(x,y)\to(-x,y)$, we get $D'(2,3)$.

Answer:

6.
Pre - Image: A(2,1), B(4,1), C(2,5)
Image: A'(2,-1), B'(4,-1), C'(2,-5)
Rule: $(x,y)\to(x,-y)$
7.
Pre - Image: A(-4,2), B(-6,3), C(-4,6), D(-2,3)
Image: A'(4,2), B'(6,3), C'(4,6), D'(2,3)
Rule: $(x,y)\to(-x,y)$