1. Why are there no invariant points under a translation ?

ALL points move the same distance and in the same direction (given by a translation vector) except when the vector has two zeroes then nothing moves!

2. Are a line and its image always parallel under a translation?


3. How many points are invariant (do not move) under translation?

None, but see question 1!

4. Is a translation an isometry?

Yes, size and shape stay the same

5. How is the translation vector found ?

Work out how far horizontally (parallel to x-axis) the object has moved then...

Work out how far vertically (parallel to y-axis) the object has moved then...

Put the first number as top number in the vector and the second number as bottom number.