Question

Consider the figure below.A (4,8) B (6,8)C (8,5)D (2,5)Part A: Reflect the Polygon ABCD over the line y=-x then rotate it 90 degress clockwise about the origin. Sktech polygon A'' B'' C'' D'' and write the coordinates below.Part B: What type of transformation(s) will carry polygon A''B'' C'' D'' back on to poly ABCD

Answer 1

Reflection of (x,y ) over y=-x is (-y, -x)

That is;

`r_(y=-x)(x,\text{ y) = (-y, -x)}`

A(4, 8) ⇒ A'(-8, -4)

B(6, 8) ⇒ B' (-8, -6)

C(8, 5) ⇒ C' (-5, -8)

D(2, 5) ⇒ D' (-5, -2)

Rotation of (x, y) clockwise about the origin over 90 degrees is (y, -x)

That is;

`R_(0,90)(x,\text{ y) = (y, -x)}`

A' (-8, -4) ⇒ A"( -4, 8)

B'(-8, -6) ⇒ B" (-6, 8)

C' (-5, -8) ⇒ C" (-8 , 5)

D' (-5, -2) ⇒ D" (-2, 5)

Part B

Reflection of the polygon A''B'' C'' D'' over y will carry the polygon to ABCD