Please Help!

How can a shape look the same after being rotated?

Question

Please Help!

How can a shape look the same after being rotated?

anonymous · Answer

won't it look the same if its rotated 360 degrees?

anonymous · Answer

Yes

anonymous · Answer

where my medal at then?

anonymous · Answer

circle

anonymous · Answer

I have 2 more questions, can you answer them?

anonymous · Answer

shoot.

kmeis002 · Answer

If its symmetric about its x/y axis, then a 180 degree rotation is guaranteed.

anonymous · Answer

4.	How does the distance from one point of the pre-image to the reflection line relate to the reflected image point? Is this relationship true for all reflections? How do you know?

anonymous · Answer

symmetric shapes such as square,

anonymous · Answer

A vector is a mathematical object that has direction and magnitude. What is another way you can describe and define a translation?

anonymous · Answer

Translation: moving all the points in the object by a vector A... I guess?

anonymous · Answer

Ok

kmeis002 · Answer

In component form, vectors are give x and y distances. Adding these distances too all points being transformed will retain its shape and hence be a true transform.

anonymous · Answer

Can you answer number 2?

anonymous · Answer

4. The distance from one point of the pre-image to the reflection line is 1/2 of distance from that point to reflected image point. This relationship holds for all reflections every point A and point on image A' are equidistant to the reflection line.

anonymous · Answer

I mean 4

kmeis002 · Answer

2 seems to be by defintion. By definition, all points on one side of the reflection line are equal distant from its imaged point. So the distance from 1 point to another is 2x where x is the distance to the line.

anonymous · Answer

Thanks!

anonymous · Answer

@kmeis002 how do you know #2? Last question

kmeis002 · Answer

Well, think of a 180 degree rotation. (images to follow). You can say a 180 degree rotation is a flip across the x axis and a flip across the y. If they are symmetric about both, it must be the same after both flips and therefore after a rotation of 180

anonymous · Answer

Huh?

kmeis002 · Answer

Sorry I was looking at 1. One moment

anonymous · Answer

Ok

kmeis002 · Answer

A vector is an object which has a X distance and  Y distance, sometimes labelled 
$$ v = <v_x , v_y>  $$
Basically, if you move a point, or series of points along the vx and the vy, there will be know rotation and it will be purely rotational. So you can describe a translation simply by adding a vector to your initial points since its magnitude is a distance. 

This means you have simply moved each point a distance the same direction.

anonymous · Answer

Lol I meant this one, just tell me how do you know.

 How does the distance from one point of the pre-image to the reflection line relate to the reflected image point? Is this relationship true for all reflections? How do you know?

anonymous · Answer

Wait I lied, can you answer the entire question for me? If not that's fine

kmeis002 · Answer

Sure, by defintion, the reflection line is the line where all points on one side (pre-image) are equal distance  from the the reflection line as the other side (image points). This means if point A has a distance of 2 from the image like, the its image point A' must also have a distance of to, so the distance between A and A' is 2+2 = 4. This works for any distance. So if A is x away from the mirror line, then A' is x away and therefore the distance between the two AA' is x+x = 2x.