Question

Grab the image of the rectangle DEFG reflection across the line x= 3​

Answer 1

Answers:

• D ' at (9, -9)
• E ' at (5, -9)
• F ' at (5, -2)
• G ' at (9, -2)

Refer to the diagram below

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Step-by-step explanation:

For points D,E,F,G we will follow these steps

1. Shift everything 3 units to the left so that the vertical line x = 3 will move on top of the y axis (which is the vertical line x = 0).
2. Reflect across the y axis using the rule
   `(x,y) \to (-x,y)`. Here we have the x coordinate flip in sign from positive to negative, or vice versa. The y coordinate stays the same.
3. Shift everything 3 units to the right so we effectively undo the first step. This places the points in the proper final position.

Let's go through an example:

Point D is located at (-3, -9). Apply the three steps mentioned above.

1. Shift point D three units to the left to arrive at (-6, -9)
2. Reflect over the y axis to go from (-6, -9) to (6, -9)
3. Lastly, shift 3 units to the right to move to (9, -9) which is the location of D'

In short, D(-3,-9) reflects over the line x = 3 to land on D ' (9, -9)

The other points E, F, G will follow the same steps to get the answers you see at the top.

The diagram below visually summarizes everything.

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Side notes:

• The distance from D to the line of reflection is the same as the distance from D' to the line of reflection. Put another way, the line of reflection bisects segment DD'. Points E,F,G follow the same property.
• Going from D to E to F to G has us go counterclockwise. Going from D' to E' to F' to G' has us go clockwise. Any reflection transformation will flip the orientation.