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5. Rhombus DEFG with vertices D(1, 4), E(5, 5), F(4, 1),

and G(0, 0); 270° clockwise rotation about R(6,8)

1 Answer

1 vote

Explanation:

First things first, we are rotating about a point so the first we do is the move the clockwise rotation to the origin.

Since a rotation is a rigid transformation, we must move all the other points as well.

So move every point using the rotation vector

R(-6,-8), move every point to

D(1-6,4-8)=D'(-5,-4)

E(5-6,5-8)=E'(-3,-5)

F(4-6,1-8)=F'(-2,-7)

G(0-6,0-8)=G'(-6,-8)

So know since the center of rotation is middle at (0,0) , we can apply the rotation rules

For a 270 clockwise rotation, we apply this rule

(-y,x)

So for the points we know get

D''(5,-4)

E''(3,-5)

F''(2,-7)

G"(6,-8)

Know since we done our rotation, we undo what we did in step 1, we add 6 to the x coordinates and 8nto the y coordinate

D"'(11,8)

E"'(9, 3)

F"(8,1)

G"'(12,0)

So those are our new coordinates.

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