Question

Choose all of the statements that correctly describe the transformation rule. Reflection over x-axis: (x, y) ? (?x, y) Reflection over y-axis: (x, y) ? (x, ?y) Rotation of 90° counter-clockwise about origin: (x, y) ? (?y, x) Rotation of 180° counter-clockwise about origin: (x, y) ? (?x, ?y) Rotation of 270° counter-clockwise about origin: (x, y) ? (y, ?x)

Answer 1

Answer:

Transformations are important subjects in geometry. In this exercise, these are the correct transformation rules:

1. Reflection over x-axis:

Consider the point $(x,y)$, if you reflect this point across the x-axis you should multiply the y-coordinate by -1, so you get:

$\boxed{(x,y)\rightarrow(x,-y)}$

2. Reflection over y-axis:

Consider the point $(x,y)$, if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:

$\boxed{(x,y)\rightarrow(-x,y)}$

3. Rotation of 90° counter-clockwise about origin:

Consider the point $(x,y)$. To rotate this point by 90° around the origin in counterclockwise direction, you can always swap the x- and y-coordinates and then multiply the new x-coordinate by -1. In a mathematical language this is as follows:

$\boxed{(x,y)\rightarrow(-y,x)}$

4. Rotation of 180° counter-clockwise about origin:

Consider the point $(x,y)$. To rotate this point by 180° around the origin, you can flip the sign of both the x- and y-coordinates. In a mathematical language this is as follows:

$\boxed{(x,y)\rightarrow(-x,-y)}$

5. Rotation of 270° counter-clockwise about origin:

Rotate a point 270° counter-clockwise about origin is the same as rotating the point 90° in clock-wise direction. So the rule is:

$\boxed{(x,y)\rightarrow(y,-x)}$