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.