An isometry is a type of transformation that preserves the length of a figure's sides. using this definition, which of the following transformations is not an isometry?
- translation
- reflection
- rotation
- stretch

Stretch

Step-by-step explanation:

- Translation: A translation moves a shape up, down or from side to side but it does not change its size.

- Reflection: A reflection is a transformation which all the points of an object reflect or flip on a line called the axis of reflection or line of reflection. This transformation does not change its size.

- Rotation: A rotation is a transformation  that turns a figure about a fixed point called the center of rotation. This transformation does not change figure's size.

- Stretch: A stretch is a transfoormation which stretch the figure (by multiplying by C>1). This transformation changes the size of the figure.

- Isometry: An isometry is a type of transformation that preserves the length of a figure's sides.

Thus, a stretch is not an isometry

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for