Transformations to Map Triangle NHY to RBT

Triangles NHY and RBT are shown on the coordinate grid.

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Which sequence of transformations will result in the triangle NHY being mapped onto triangle RBT ?

(x,y)→(x, y+3) then (x,y)→(x, −y) then (x,y)→(1.5x, 1.5y)

(x,y)→(1.5x, 1.5y) then (x,y)→(x, −y) then (x,y)→(x, y+3)

(x,y)→(x, y+3) then (x,y)→(0.5x, 0.5y) then (x,y)→(−x, y)

(x,y)→(0.5x, 0.5y) then (x,y)→(−x, y) then (x,y)→(x, y+3)

To determine which sequence of transformations maps triangle NHY onto triangle RBT, we need to analyze the transformations step by step.

1. Translation: Moving the triangle up or down, left or right.
2. Reflection: Flipping the triangle over a line (e.g., the x-axis or y-axis).
3. Dilation: Resizing the triangle (enlarging or reducing).

Let's break down the options provided:

1. Option 1:

   • (x,y)→(x, y+3): This translates the triangle up by 3 units.
   • (x,y)→(x, −y): This reflects the triangle over the x-axis.
   • (x,y)→(1.5x, 1.5y): This dilates the triangle by a factor of 1.5.

2. Option 2:

   • (x,y)→(1.5x, 1.5y): This dilates the triangle by a factor of 1.5.
   • (x,y)→(x, −y): This reflects the triangle over the x-axis.
   • (x,y)→(x, y+3): This translates the triangle up by 3 units.

3. Option 3:

   • (x,y)→(x, y+3): This translates the triangle up by 3 units.
   • (x,y)→(0.5x, 0.5y): This reduces the triangle by a factor of 0.5.
   • (x,y)→(−x, y): This reflects the triangle over the y-axis.

4. Option 4:

   • (x,y)→(0.5x, 0.5y): This reduces the triangle by a factor of 0.5.
   • (x,y)→(−x, y): This reflects the triangle over the y-axis.
   • (x,y)→(x, y+3): This translates the triangle up by 3 units.

To find the correct sequence, we need to consider the positions of the triangles NHY and RBT on the coordinate grid.

• If triangle NHY is smaller and needs to be enlarged to match triangle RBT, we would need a dilation (enlargement).
• If triangle NHY is positioned differently, we would need a translation to move it to the correct location.
• If the orientation of the triangles is different, we would need a reflection.

Without the specific coordinates of triangles NHY and RBT, I can't definitively determine which option is correct. However, if you analyze the transformations based on the size, position, and orientation of the triangles, you can identify the correct sequence.

If you can provide the coordinates or a description of the triangles' positions, I can help you determine the