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1. A triangle XYZ with coordinates X (5,8), Y(3,1), 2(1,6) is translated 3 units left, 2 units up, thenrotated 90 degrees clockwise about the origin. What are the coordinates for X', Y, and Z?

Answer :

Recall the following rules for the given geometric transformations.

Translation c units left:

[tex](x,y)\rightarrow(x-c,y)[/tex]

Translation c units up:

[tex](x,y)\rightarrow(x,y+c)[/tex]

Rotation 90 degrees clockwise about the origin:

[tex](x,y)\rightarrow(y,-x)[/tex]

Then, the combination of a translation 3 units left, 2 units up and a rotation 90 degrees clockwise about the origin, is given by the rule:

[tex](x,y)\rightarrow(x-3,y)\rightarrow(x-3,y+2)\rightarrow(y+2,-x+3)[/tex]

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