Question

reflections

1. $r_m\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$ and line $m$ is $y = x$.

$a(0,3)$ $b(3,5)$ $c(6,7)$

1. $r_m\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$ and line $m$ is $y = 0$.

$a(3,0)$ $b(5, - 3)$ $c(7,-6)$

1. $r_m\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$ and line $m$ is $x = 0$.

$a(-3,0)$ $b(-5,3)$ $c(-7,6)$

1. $r_m\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$ and line $m$ is $y=-x$.

Explanation:

Step1: Recall reflection rule for $y = -x$

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

Step2: Reflect point A

For point $A(3,0)$, applying the rule $(x,y)\to(-y,-x)$, we get $A'(0, - 3)$.

Step3: Reflect point B

For point $B(5,3)$, applying the rule $(x,y)\to(-y,-x)$, we have $B'(-3,-5)$.

Step4: Reflect point C

For point $C(7,6)$, applying the rule $(x,y)\to(-y,-x)$, we obtain $C'(-6,-7)$.

Answer:

$A'(0, - 3), B'(-3,-5), C'(-6,-7)$