Question

1. translation: (x, y) → (x - 7, y + 3)
2. rotation 180° about the origin
3. reflection across x = -3
4. translation: (x, y) → (x + 2, y)
5. translation: (x, y) → (x, y - 1)
6. rotation 180° about the origin

Explanation:

Step1: Identify the transformation type

The problem (let's take problem 10 as an example: translation \((x, y) \to (x + 2, y)\)) involves transforming a figure on a coordinate plane. This is a topic in Geometry (subfield of Mathematics) dealing with rigid transformations (translations, rotations, reflections).

Step2: Apply the translation rule

For a translation \((x, y) \to (x + 2, y)\), each point \((x,y)\) of the original figure (e.g., the vertices of the quadrilateral in problem 10) will have its \(x\)-coordinate increased by 2 and \(y\)-coordinate remain the same. So, if a vertex has coordinates \((x_1,y_1)\), the new coordinates will be \((x_1 + 2,y_1)\). We do this for all vertices of the figure and then plot the new points to get the translated figure.

(Note: Since the specific question about which problem to solve isn't clear, this is a general approach for translation problems like the ones shown. For other problems like reflection or rotation, similar steps apply: identify the transformation rule, apply it to each vertex's coordinates, and plot the new figure.)

Answer:

(For a specific problem, e.g., problem 10 translation: The translated figure is obtained by moving each vertex of the original figure 2 units to the right (since \(x\)-coordinate increases by 2, \(y\)-coordinate unchanged). The exact coordinates depend on the original figure's vertices, but the process is as explained above.)