What is Reflection, Translation, and Rotations?

Answer 1

Let's say you have a letter R written on a piece of paper and drew a vertical line to the right of it. If you reflect the R over the line, you would get a backwards R on the other side of the line. When you do a reflection, each point makes a new point on the other side of the line at the same distance from the line as the original point.

Translation is easy: keep the object facing the same direction, and just scoot it across the paper. Your R would still be right side up and not backwards, just in a new place.

Rotations are like if you took that R and taped it to the end of the minute hand of a clock, and let the clock hand spin around. The R is rotating about the center of the clock. At the "15 minute" position, the R would be tipped over on its round side, at the "30 minute" position, it would be upside down, but not a reflected kind of upside down, a rotated kind of upside down.

Answer 2

Given that you've stated these together you are probably looking for the algebraic definition. A matrix can specify a reflection translation or rotation of an input vector. A reflection mirrors the vector (usually across an axis). A translation moves the vector in space. A rotation changes the angle the vector makes with the axes. I think there are ways to combine these actions... I seem to vaguely recall something from university on this.

Answer 3

actually, i just got done doing those recently in my geometry class
reflection is where some thing is reflected across the x-axis the y-axis or the line x=y. it would be like using a miror and just reflecting the abject on the graph. actually i actually used something on my homework that showed me what the object looked like reflected, then you just have to draw it. try using a mirror.
translation is where each point of the object is moved up, down, to the side, etc.
rotation is where the point or object is just rotated on the graph (its kinda hard to explain) kind of like the hand of a clock rotates. when the hand goes from the 12 to the 6, it has rotated 180 degrees (i think)

I'm still not sure if I get all of this so I hope my information is correct but I'm pretty sure that is what they are

hope it helps

Answer 4

The three algebraic transformations.

A reflection is a mirroring across a line. Translation is moving an object respective to the origin. Rotation is a twisting about a point.

Answer 5

Reflection in 2 dimensions means that there is a line (think of it as representing a mirror) so that the image of each point in the reflected figure is on the opposite side of the line, same distance away as the reflected point, with the join of the point and its image at rightangles to the line. i.e. move the point at rightangles to the line to a position the same distance on the other side.

In coordinates, you can reflect in the x axis by changing the sign of the y coordinate (and vice-versa); you can reflect in the line y=x by swapping the (x, y) coordinates with each other, etc.

Translation means every point moves the same distance in the same direction, i.e. you just slide the figure across the plane without turning it at all. In coordinates, add a constant value to every x coordinate, and another constant value to every y.

Rotation means you have a fixed centre of rotation, and every point moves the same number of degrees around this centre. So you might rotate a figure through 40 deg about a fixed centre. The points nearer to the centre would move in a smaller radius than the furthest points, but all of them would swing through a 40 deg arc (but usually with different radii). The direction the rotated figure faces is at 40 deg to its original direction too.

I just had a look at Jen's answer, and I think it's the best.

Answer 6

Reflection is an activity in computation that allows an object to have information about the structure and reason about its own computation.
Translation is an activity comprising the interpretation of the meaning of a text in one language.
Rotation is the movement of an object in a circular motion.

Answer 7

The three ways a shape can be moved in geometry.
Reflection is changing it to what you woul see in a mirror.
Translation just means moving (like left, right etc.).
Rotation means spinning it.

Answer 8

the three algebraic transformations