Question

complete the mapping of the vertices of △def. d(2, -4)→ e(1, -1)→ f(5, 1)→ 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: Map point D

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

Step3: Map point E

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

Step4: Map point F

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

Step5: Determine the general rule

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

Answer:

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