A translation is a transformation that moves every point of a figure the same distance and the same direction.
According to this definition, each point in the image created by a translation moves the same distance and direction from the preimage.
Therefore, the first statement is true.
Second Statement
To determine whether the second statement is true, we will look at an example of a translation.
Figure A' is an image of Figure A and point K' is an image of point K. We can see that K and K' do not have the same x-coordinate. This means that the second statement is not true.
Third and Fourth Statements
Now we will determine whether the third and the fourth statements are true. To do so, let's recall the properties of the figure after a translation.
An image of a figure after a translation has the same shape, size, and orientation as the figure.
According to this fact, the preimage and the image are the same size and shape. Let's convince how it works by looking at the example!
We can see that Figure A did not change its shape and size after the translation. Therefore, the third and the fourth statements are true.
