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Use the image to answer the question. A B C OR D which one is it oh my god please help me ace this test

Two quadrilaterals upper A upper B upper C upper D and upper E upper F upper G upper H are marked in the second and fourth quadrants of a coordinate plane respectively.

What reflections or sequence of reflections transforms figure ABCD into figure EFGH?

(1 point)
Responses

Reflect ABCD first over the line x=0
, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line x is equal to 0, then over the line y is equal to x .

Reflect ABCD first over the line y=0, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line y is equal to 0 , then over the line y is equal to x .

Reflect ABCD first over the line x=0, then over the line y=0.
Reflect cap A cap b cap c cap d first over the line x is equal to 0 , then over the line y is equal to 0 .

Reflect ABCD over the line y=x
Reflect cap A cap b cap c cap d over the line y is equal to x
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1 answer

To determine the correct sequence of reflections that transforms quadrilateral ABCD into quadrilateral EFGH, we will analyze the transformations based on the properties of reflections over the specified lines.

  1. Reflecting over the line \(x = 0\) (the y-axis) will change the x-coordinates of the points from positive to negative or vice-versa, while keeping the y-coordinates the same. This reflection flips the shape horizontally.

  2. Reflecting over the line \(y = x\) will swap the x and y-coordinates of the points. This reflection rotates the shape around the line \(y = x\).

  3. Reflecting over the line \(y = 0\) (the x-axis) will change the y-coordinates of the points from positive to negative or vice versa while keeping the x-coordinates the same. This reflection flips the shape vertically.

Based on these properties, you need to check how the corners of ABCD would be positioned relative to EFGH after these transformations.

Here are some options we need to analyze based on the sequence of reflections:

  • First option: Reflect ABCD first over the line \(x = 0\) then over the line \(y = x\).
  • Second option: Reflect ABCD first over the line \(y = 0\) then over the line \(y = x\).
  • Third option: Reflect ABCD first over the line \(x = 0\) then over the line \(y = 0\).
  • Fourth option: Reflect ABCD over the line \(y = x\).

You would need to visually check which sequence of transformations correctly matches ABCD to EFGH by considering the location of each point (A, B, C, D) before and after each reflection.

If you can visualize or sketch the transformations, the correct reflection sequence should be evident. Please take these details into account and choose the option that matches your findings.