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#REFLECTION RULES GEOMETRY CALCULATOR HOW TO#
#REFLECTION RULES GEOMETRY CALCULATOR FULL#

Now I want you to try some practice problems on your own. Let’s apply the rules to the vertices to create quadrilateral A’B’C’D’: To rotate quadrilateral ABCD 90° counterclockwise about the origin we will use the rule (x,y) becomes (-y,x). Let’s apply the rule to the vertices to create the new triangle A’B’C’: Let’s rotate triangle ABC 180° about the origin counterclockwise, although, rotating a figure 180° clockwise and counterclockwise uses the same rule, which is (x,y) becomes (-x,-y), where the coordinates of the vertices of the rotated triangle are the coordinates of the original triangle with the opposite sign. To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x), where the y-value of the original point becomes the new x-value and the x-value of the original point becomes the new y-value with the opposite sign.

#REFLECTION RULES GEOMETRY CALCULATOR HOW TO#

Now that we know how to rotate a point, let’s look at rotating a figure on the coordinate grid.

270° counterclockwise rotation: (x,y) becomes (y,-x)Īs you can see, our two experiments follow these rules.

270° clockwise rotation: (x,y) becomes (-y,x).

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

90° counterclockwise rotation: (x,y) becomes (-y,x).

90° clockwise rotation: (x,y) becomes (y,-x).

Lucky for us, these experiments have allowed mathematicians to come up with rules for the most common rotations on a coordinate grid, assuming the origin, (0,0), as the center of rotation. In our second experiment, point A (5,6) is rotated 180° counterclockwise about the origin to create A’ (-5,-6), where the x- and y-values are the same as point A but with opposite signs. In our first experiment, when we rotate point A (5,6) 90° clockwise about the origin to create point A’ (6,-5), the y-value of point A became the x-value of point A’ and the x-value of point A became the y-value of point A’ but with the opposite sign. Let’s take a closer look at the two rotations from our experiment. Here is the same point A at (5,6) rotated 180° counterclockwise about the origin to get A’(-5,-6). Let’s look at a real example, here we plotted point A at (5,6) then we rotated the paper 90° clockwise to create point A’, which is at (6,-5). If you take a coordinate grid and plot a point, then rotate the paper 90° or 180° clockwise or counterclockwise about the origin, you can find the location of the rotated point. Let’s start by looking at rotating a point about the center (0,0). Here is a figure rotated 90° clockwise and counterclockwise about a center point.Ī great math tool that we use to show rotations is the coordinate grid.

We specify the degree measure and direction of a rotation. The angle of rotation is usually measured in degrees. The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. Another great example of rotation in real life is a Ferris Wheel where the center hub is the center of rotation. A figure can be rotated clockwise or counterclockwise. A figure and its rotation maintain the same shape and size but will be facing a different direction. We call this point the center of rotation. More formally speaking, a rotation is a form of transformation that turns a figure about a point.

#REFLECTION RULES GEOMETRY CALCULATOR FULL#

There are other forms of rotation that are less than a full 360° rotation, like a character or an object being rotated in a video game. The wheel on a car or a bicycle rotates about the center bolt.

The earth is the most common example, rotating about an axis. Hello, and welcome to this video about rotation! In this video, we will explore the rotation of a figure about a point.