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Question

Two quadrilaterals upper A ( 1,-5) upper B (5,-2) upper C (8,-2) upper D (7,-4) and upper E (-5,1) upper F (-2,5) upper G (-2,8) upper H (-4,7) 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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Answer 1

To determine the reflections that transform figure ABCD into figure EFGH, let's analyze the coordinates of the points in both figures.

Coordinates:

• ABCD:

  • A(1, -5)
  • B(5, -2)
  • C(8, -2)
  • D(7, -4)

• EFGH:

  • E(-5, 1)
  • F(-2, 5)
  • G(-2, 8)
  • H(-4, 7)

Now, let's identify the transformations needed.

1. Reflect over the line x=0 (the y-axis):

   • This will change the sign of the x-coordinates.
   • New Coordinates after reflection:
     • A'(-1, -5)
     • B'(-5, -2)
     • C'(-8, -2)
     • D'(-7, -4)

2. Next, reflect over the line y=0 (the x-axis):

   • This will change the sign of the y-coordinates.
   • New Coordinates after this second reflection:
     • A''(-1, 5)
     • B''(-5, 2)
     • C''(-8, 2)
     • D''(-7, 4)

3. Lastly, reflect over the line y=x:

   • This will swap the x and y coordinates.
   • New Coordinates after this reflection:
     • A'''(5, -1)
     • B'''(2, -5)
     • C'''(2, -8)
     • D'''(4, -7)

From the first two reflections, we can see that the shape is being moved from one quadrant to another, but to confirm the final position, reflecting over y=x effectively places the points into their corresponding positions in figure EFGH.

Thus, the correct sequence of transformations is:

Reflect ABCD first over the line y=0, then over the line y=x.

So, the correct response is: Reflect ABCD first over the line y=0, then over the line y=x.