Question

Triangle CAT was rotated to create triangle C'A'T'. Describe the transformation using details and degrees.

Answer 1

Notice that A is 1 unit to the left of and two above C, while A' is two to the right of and 1 above. You can describe the rotation of the triangle *about* C (keeping C still and moving things around it) by drawing a circle with C at the center and A at the edge; then you can more easily find how many degrees the triangle was "rotated through." Then you can also use C as a judge of the translation (it's 1 up and three to the right of where it started). Lastly if two circles are drawn with 1 inside the other with the same origin, they're called concentric ("con" meaning "with" or "join," and centric as in "center" ).

Answer 2

The triangle CAT is rotated 90 degree clockwise direction about the origin or 270 degree counterclockwise direction about the origin.

Explanation:

From the given figure it is noticed that the coordinates of vertices of pre-image are C(-2,1), A(-3,3) and T(1,1). The coordinates of vertices of image are C'(1,2), A'(3,3) and T(1,-1).

From these coordinates we can conclude that the relation between preimage and image is

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

If a figure rotated 90 degree clockwise direction about the origin, then

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

`C(-2,1)\rightarrow C'(1,2)`

`A(-3,3)\rightarrow A'(3,3)`

`T(1,1)\rightarrow T'(1,-1)`

Therefore triangle CAT is rotated 90 degree clockwise direction about the origin or 270 degree counterclockwise direction about the origin.