Question

d ( box, box )
e ( , )
f ( , )
g ( , )

Explanation:

To solve for the coordinates of the transformed points \( D' \), \( E' \), \( F' \), and \( G' \), we first need to determine the original coordinates of points \( D \), \( E \), \( F \), and \( G \) from the graph.

Step 1: Identify Original Coordinates

• Point \( D \): From the graph, \( D \) is at \( (2, -9) \) (since it's 2 units right on the x - axis and 9 units down on the y - axis).
• Point \( E \): \( E \) is at \( (8, -9) \) (8 units right on the x - axis and 9 units down on the y - axis).
• Point \( F \): \( F \) is at \( (8, -3) \) (8 units right on the x - axis and 3 units down on the y - axis).
• Point \( G \): \( G \) is at \( (2, -3) \) (2 units right on the x - axis and 3 units down on the y - axis).

Step 2: Determine the Transformation (Assuming a Common Transformation, e.g., Translation or Reflection; Since the Problem is Incomplete, Let's Assume a Translation or Just State the Process)

If we assume a transformation (for example, if we were to translate the figure, say, 3 units left and 2 units up, but since the problem doesn't specify, we'll show the general process). However, since the problem is likely about identifying coordinates (maybe after a transformation like reflection over an axis or translation), let's assume we need to find coordinates (maybe the problem was about a specific transformation, but since it's not given, we'll present the original coordinates and the process).

Wait, maybe the problem was about reflecting over the y - axis or x - axis. Let's check the grid. If we reflect over the y - axis (\( (x,y)\to(-x,y) \)):

• \( D(2, -9)\to D'(-2, -9) \)
• \( E(8, -9)\to E'(-8, -9) \)
• \( F(8, -3)\to F'(-8, -3) \)
• \( G(2, -3)\to G'(-2, -3) \)

Or if it's a translation. Since the problem is not fully specified, but based on the grid, let's assume the original coordinates first:

Original coordinates:

• \( D(2, -9) \)
• \( E(8, -9) \)
• \( F(8, -3) \)
• \( G(2, -3) \)

If we assume a translation (for example, moving 5 units left and 0 units up, but this is speculative). However, since the problem's context is about coordinate geometry (subfield of Mathematics - Geometry), we'll present the original coordinates and the process of finding transformed coordinates.

Final Answer (Assuming Original Coordinates or a Common Transformation, e.g., Reflection over y - axis)

If reflection over y - axis:

• \( D'(-2, -9) \)
• \( E'(-8, -9) \)
• \( F'(-8, -3) \)
• \( G'(-2, -3) \)

If the problem was about identifying the original coordinates (maybe a typo), then:

• \( D(2, -9) \)
• \( E(8, -9) \)
• \( F(8, -3) \)
• \( G(2, -3) \)

Since the problem is incomplete, but based on the grid, the original coordinates are:
\( D(2, -9) \), \( E(8, -9) \), \( F(8, -3) \), \( G(2, -3) \)

If we assume a transformation (e.g., reflection over y - axis), the transformed coordinates are:
\( D'(-2, -9) \), \( E'(-8, -9) \), \( F'(-8, -3) \), \( G'(-2, -3) \)

(Note: The problem was incomplete, but this is the best attempt based on the given graph. If you can provide more details about the transformation, we can give a more accurate answer.)

Answer:

(Assuming Original Coordinates)

• \( D(2, -9) \)
• \( E(8, -9) \)
• \( F(8, -3) \)
• \( G(2, -3) \)

(If the problem was about a specific transformation, please provide more details.)