To solve problems with shapes that change in different ways, it’s important to know how each type of change affects the points of the shape. The changes we often talk about include moving (translations), turning (rotations), flipping (reflections), and resizing (enlargements).

1. Translations are when we move a shape a certain distance in a certain direction.

   • For example, if we move the point $(2, 3)$ to the right by 4 units, it will be at $(6, 3)$.

2. Rotations need a center point and an angle to turn.

   • For example, if we turn the point $(1, 0)$ 90 degrees to the left around the center point (the origin), it will change to $(0, 1)$.

3. Reflections are like flipping a shape over a line. When we reflect a point across the x-axis, we change its y-coordinate.

   • So, if we reflect the point $(3, 4)$ across the x-axis, it will become $(3, -4)$.

4. Enlargements involve making a shape bigger using a scale factor and a center point.

   • If we enlarge the point $(2, -1)$ by a scale factor of 2, using the origin as the center, it turns into $(4, -2)$.

By doing each of these changes one after the other, you can figure out where the shape will end up on a graph. Just remember to keep track of how each change affects the position of the points!