Question

I can't really identify what type of transformation it is

Answer 1

The original point is: (4, 1)

First transformation:

After the first transformation (4,1) becomes (1,4).

This transformation is a reflection across the line y=x. Because the rule for a reflection across the line y=x is:

`(x,y)\longrightarrow(y,x)`

Since after the transformation the point (4,1) became (1,4), we can see that the x coordinate was interchanged with the y coordinate.

Thus, the transformation that occurred here was a reflection across the line y=x.

Second transformation:

The previous point was (1,4) and with this second transformation, it became the point (1,-4). The x coordinate is the same, but the y coordinate changed its sign to a negative sign. The transformation that occurred here is: Reflection across the x-axis.

Because the rule for a reflection across the x-axis is:

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

The x coordinate stays the same, and the y coordinate changes its sign.

Thus, the transformation was: a reflection across the x-axis.

Third transformation:

The previous point was (1,-4) and after the third transformation, the point is (-1,4). As you can see both the x-coordinate and the y-coordinate changed sign. The transformation is: a rotation of 180° about the origin.

Because the rule for this rotation is:

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

Both coordinates change of sign.

Thus, the transformation in this part was: rotation of 180° about the origin.

Answer:

reflection across the line y=x.

reflection across the x-axis.

rotation of 180° about the origin.