Question

a reflection flips the figure over a line to create a mirror image.
a rotation turns the figure around a point.
a translation slides the figure to a different location.
use a rotation to turn shape 1 into shape 2. this image shows a
rotation. rotate the shape 180°.
use a translation to turn shape 2 into shape 3. this image shows a
translation. translate the shape up 4 and right 5.
to go from shape 1 to shape 2 to shape 3, use a rotation and then
a translation.

Explanation:

Step1: Rotate Shape 1 180°

To rotate a shape 180° around a point (usually the center of rotation, here the common vertex or a central point), each vertex \((x,y)\) of Shape 1 transforms to \((-x + 2h, -y + 2k)\) where \((h,k)\) is the center of rotation. Visually, this flips the shape both horizontally and vertically, matching the position and orientation of Shape 2.

Step2: Translate Shape 2 up 4 and right 5

For a translation, each vertex \((x,y)\) of Shape 2 moves to \((x + 5, y + 4)\). Moving up 4 increases the \(y\)-coordinate by 4, and moving right 5 increases the \(x\)-coordinate by 5, resulting in the position of Shape 3.

Answer:

The transformation from Shape 1 to Shape 2 is a \(180^\circ\) rotation, and from Shape 2 to Shape 3 is a translation (up 4, right 5). The combined transformation is rotation then translation as described.