Question

1. reflect over the x - axis

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

1. (x,y)→( - x,y)

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

1. (x,y)→(x, - y)

pre - image image description:
a(0,0) a(\t,\t)
b(1, - 2) b(\t,\t)
c( - 4, - 1) c(\t,\t)
d( - 3, - 3) d(\t,\t)
write a rule that represents each reflection of the arrows below.
11.
12.

Explanation:

Step1: Recall reflection rules

When reflecting a point $(x,y)$ over the $x - axis$, the rule is $(x,y)\to(x, - y)$. When the rule is $(x,y)\to(-x,y)$, it is a reflection over the $y - axis$. When the rule is $(x,y)\to(x,-y)$, it is a reflection over the $x - axis$.

Step2: Solve problem 8

For point $A(4,1)$ reflected over the $x - axis$, using the rule $(x,y)\to(x, - y)$, we get $A'(4,-1)$. For $B(2, - 1)$, $B'(2,1)$. For $C(2,-4)$, $C'(2,4)$. For $D(4,-4)$, $D'(4,4)$. The rule is $(x,y)\to(x,-y)$.

Step3: Solve problem 9

Given the rule $(x,y)\to(-x,y)$ (reflection over the $y - axis$). For $A(0,3)$, $A'(0,3)$. For $B(6,5)$, $B'(-6,5)$. For $C(2,5)$, $C'(-2,5)$. The description is "Reflection over the y - axis".

Step4: Solve problem 10

Given the rule $(x,y)\to(x,-y)$ (reflection over the $x - axis$). For $A(0,0)$, $A'(0,0)$. For $B(1,-2)$, $B'(1,2)$. For $C(-4,-1)$, $C'(-4,1)$. For $D(-3,-3)$, $D'(-3,3)$. The description is "Reflection over the x - axis".

Answer:

Problem 8:

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

Problem 9:

Pre - Image	Image	Description
$B(6,5)$	$B'(-6,5)$
$C(2,5)$	$C'(-2,5)$

Problem 10:

Pre - Image	Image	Description
$B(1,-2)$	$B'(1,2)$
$C(-4,-1)$	$C'(-4,1)$
$D(-3,-3)$	$D'(-3,3)$