Question

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 1

Recall the following rules for the given geometric transformations.

Translation c units left:

`(x,y)\rightarrow(x-c,y)`

Translation c units up:

`(x,y)\rightarrow(x,y+c)`

Rotation 90 degrees clockwise about the origin:

`(x,y)\rightarrow(y,-x)`

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:

`(x,y)\rightarrow(x-3,y)\rightarrow(x-3,y+2)\rightarrow(y+2,-x+3)`