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 90° clockwise.
use a translation to turn shape 2 into shape 3. this image shows a translation. translate the shape down 4 and left 3.
to go from shape 1 to shape 2 to shape 3, use a rotation and then a translation.

Explanation:

Step1: Rotate Shape 1 90° clockwise

Identify the key points of Shape 1 (the blue figure). For a 90° clockwise rotation about a point (usually the intersection point or a vertex, here we can take the common vertex with Shape 2), the rotation rule is \((x,y) \to (y, -x)\) (adjusting for grid coordinates, moving each point 90° clockwise around the center of rotation). After rotating each vertex, we get the position of Shape 2 (the purple figure).

Step2: Translate Shape 2 down 4 and left 3

Take the vertices of Shape 2. For a translation down 4, we subtract 4 from the y - coordinate of each vertex, and for a translation left 3, we subtract 3 from the x - coordinate of each vertex. Applying this to all vertices of Shape 2 gives the position of Shape 3 (the yellow figure).

Answer:

The transformation from Shape 1 to Shape 3 is achieved by first rotating Shape 1 90° clockwise to get Shape 2, and then translating Shape 2 down 4 units and left 3 units to get Shape 3. (If a graphical answer is expected, the rotated and translated figure as per the above steps is the result.)