Triangles def and d'e'f' are shown on the coordinate plane below: triangle def and triangle d prime e prime f prime with ordered pairs at d negative 1, 6, at e 1, 3, at f 6, 3, at d prime 6, 1, at e prime 3, negative 1, at f prime 3, negative 6. what rotation was applied to triangle def to create triangle d'e'f'?

Rotation of 90° clockwise applied to triangle DEF.

Step-by-step explanation:

Given : Triangles DEF and D'E'F' are shown on the coordinate plane below.

To find : What rotation was applied to triangle DEF to create triangle D'E'F'?

Solution : We have given that triangles DEF and D'E'F'.

Coordinates of D (-1, 6)  ; E ( 1, 3) and F( 6, 3) .

Coordinates of D' (6, 1)  ; E' ( 3, -1) and F'( 3, -6) .

By the rotational rule of  90° clockwise ( x, y)→→( y , -x).

Then we can D (-1, 6) →→ D' (6, 1) .

                    E ( 1, 3) →→  E' ( 3, -1).

                  F( 6, 3)→→F'( 3, -6) .

Therefore, Rotation of 90° clockwise applied to triangle DEF.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c