Polygon ABCDEF is rotated 90°, reflected across the line y = -x, and then translated up 3 units and to the left 2 units to produce the image polygon A'B'C'D'EF'. What are the
coordinates of D' ?

D'(-4, 1)

Step-by-step explanation:

Polygon ABCDEF is transformed by number of steps given in the question.

We have to find the coordinates of point D'.

Coordinates of point D → (2, -2)

Step - 1,

Polygon rotated 90° counterclockwise about the origin,

Rule for this rotation,

(x, y) → (-y, x)

Coordinates of image E after rotation,

D(2, -2) → E(2, 2)

Step - 2,

Point E then reflected across the line y = -x,

Rule for the reflection,

(x, y) → (-y, -x)

Image of E after reflection will be,

E(2, 2) → F(-2, -2)

Step -3,

Then point F was translated up by 3 units and 2 units left,

Rule for the translation,

(x, y) → (x -2, y + 3)

Image of F will be point D',

F(-2, -2) → D'(-4, 1)

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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answer: huh

step-by-step explanation: