# How do you rotate a shape 45 degrees?

If we represent the point (x,y) by the complex number x+iy, then we can rotate it 45 degrees clockwise simply by multiplying by the complex number (1−i)/√2 and then reading off their x and y coordinates. (x+iy)(1−i)/√2=((x+y)+i(y−x))/√2=x+y√2+iy−x√2. Therefore, the rotated coordinates of (x,y) are (x+y√2,y−x√2).

## How do you rotate a shape degrees?

Cool, let’s start then with some easy general rules.

1. When rotating a shape by 90 degrees about the origin, each point (x,y) becomes (-y,x)
2. When rotating a shape by 180 degrees about the origin, each point (x,y) becomes (-x,’-y)
3. When rotating a shape by 270 degrees about the origin, each point (x,y) becomes (y, -x)

## How do you rotate angles?

1. The point of rotation is the origin, draw lines joining one of the points, say X and it’s image to the origin.
2. You can see that the lines form an angle of 270° , in the counterclockwise direction.
3. Therefore, ΔX’Y’Z’ is obtained by rotating ΔXYZ counterclockwise by 270° about the origin.
4. So, the correct choice is C .
Read more  Do you write three or 3?

## What is the rule for a 90 degree rotation?

Rules of Rotation

The general rule for rotation of an object 90 degrees is (x, y) ———> (-y, x). You can use this rule to rotate a pre-image by taking the points of each vertex, translating them according to the rule, and drawing the image.

## What is the formula for rotating 90 degrees counterclockwise?

90 Degree Rotation

When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

## How do you describe a rotation?

A Rotation Can Be Described as Both Clockwise and Counter-Clockwise. The rotation below can be described as both 90° clockwise and 270° counter-clockwise: If a rotation is θ clockwise, it is 360 − θ counter-clockwise.

## What is the angle of rotation of circle?

In mathematics, the angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle. … If a cart moves around the wheel once, the angle of rotation is 360°.

## What is the angle of rotation of a regular pentagon?

The order of rotational symmetry of a regular pentagon is 5. The angle of rotation is 72º.

## What is the order and angle of rotation?

The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself. The order of symmetry is the number of times the figure coincides with itself as its rotates through 360° . Example: … The angle of rotation is 60° and the order of the rotational symmetry is 6 .

## What is the rule for 360 degree rotation?

360° Rotation A rotation of 360° about a point returns a figure to its original position. That is, the image under a 360° rotation is equal to the preimage. Copy each figure and point K. Then use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.