Question

complete the mapping of the ver
d(2, -4) → d
e(1, -1) → e
f(5, 1) → f
what is the rule that describes a reflection across the line y = x?
r_x = y(x, y) →

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the line $y = x$, the $x$ - and $y$ - coordinates are swapped.

Step2: Find $D'$

For point $D(2,-4)$, after reflection across $y = x$, $D'$ is $(-4,2)$.

Step3: Find $E'$

For point $E(1,-1)$, after reflection across $y = x$, $E'$ is $(-1,1)$.

Step4: Find $F'$

For point $F(5,1)$, after reflection across $y = x$, $F'$ is $(1,5)$.

Step5: State the rule

The rule for reflection across the line $y = x$ is $r_{y = x}(x,y)\to(y,x)$.

Answer:

$D(2,-4)\to D'(-4,2)$
$E(1,-1)\to E'(-1,1)$
$F(5,1)\to F'(1,5)$
$r_{y = x}(x,y)\to(y,x)$