Complete the mapping of the vertices of ΔDEF. 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? rx = y(x, y) →

The rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.

What is reflection?

The reflection of a plane or shape is flipping the original figure with respect to a reference line.

The following steps are used to for reflecting a shape-

Select the shape which has to be reflected.
Select a base line or reference line over which the shape has to be reflected.
Mark the corners of the shape at the equidistant from the reference line as the original shape has, but in the opposite direction.
The reflected shape is now is facing the opposite direction.

The rule that describes a reflection across the line says that when your reflect a point across the line say y=x. Then the coordinates of x and y are interchanged as,

y(x, y) → (y, x)

Now let's complete the mapping of the vertices of ΔDEF using the above rule. For this, change the places of x and y coordinate as,

D(2, –4) → (-4, 2)D'

E(1, –1) → (-1, 1)E'

F(5, 1) → (1, 5)F'

Thus, the rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.

Learn more about the reflection here;

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