Question

what are the coordinates of the image after the reflection in the given line.
$y = -x$
a(
,
)
b(
,
)
c(
,
)
d(
,
)

Explanation:

Step1: Recall reflection rule

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

Step2: Find A'

Point A has coordinates $(3,1)$. Using the rule, $x = 3$ and $y=1$, so $A'\to(-1,-3)$.

Step3: Find B'

Point B has coordinates $(2,1)$. Using the rule, $x = 2$ and $y = 1$, so $B'\to(-1,-2)$.

Step4: Find C'

Point C has coordinates $(1,0)$. Using the rule, $x = 1$ and $y = 0$, so $C'\to(0,-1)$.

Step5: Find D'

Point D has coordinates $(2,2)$. Using the rule, $x = 2$ and $y = 2$, so $D'\to(-2,-2)$.

Answer:

A'(-1, -3)
B'(1, -2)
C'(0, -1)
D'(-2, -2)