Question

complete the mapping of the vertices of △def. 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

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

Step2: Map point D

For $D(2,-4)$, applying the rule $(x,y)\to(y,x)$ gives $D'(-4,2)$.

Step3: Map point E

For $E(1,-1)$, applying the rule gives $E'(-1,1)$.

Step4: Map point F

For $F(5,1)$, applying the rule gives $F'(1,5)$.

Step5: State the general rule

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

Answer:

D'(-4,2)
E'(-1,1)
F'(1,5)
$(y,x)$