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Sagot :
Answer: All four answer choices would create congruent shapes.
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Explanation:
Reflections, rotations, and translations are considered rigid transformations. What this means is that they keep the same shape, but the shape has been moved in some fashion. As such, the "before" (preimage) and "after" (image) are congruent figures.
Imagine you drew a triangle on a clear piece of glass. If you took a picture of it from one side, then took another picture from the opposite side, then you'd get reflected versions of the triangle. Notice how the triangle has not moved at all. The camera has. Therefore, this proves that reflections keep the same exact shape. The only thing different is the orientation has swapped.
Now imagine you drew a triangle etched in stone. Grab your camera to take a picture of it. Then rotate the camera to get another picture. The two triangles are rotated copies of each other. They're the same exact triangle since the figure etched in stone hasn't changed. Only the camera has. This thought exercise proves rotations are a rigid transformation, aka an isometry.
Lastly, we'll go back to the triangle etched in stone to work with translations. A translation is any shifting. Take a picture of the triangle etched in stone. Then move the camera around to pan to another location (panning is when you keep your aim at the subject but move side to side, or up and down). Imagine the camera is stuck on a train track and can only aim one direction. The camera will take two pictures of the same triangle, of course the only difference is that they have shifted in the frame. Therefore, translations are the third final type of rigid transformation.
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Dilations are not rigid transformations, but only if the scale factor was something else than 1.
If the scale factor is less than 1, then the image shrinks.
If the scale factor is greater than 1, then the image enlarges.
If the scale factor is exactly 1, then the image doesn't change at all. This is because we multiplied all sides by 1. Multiplying by 1 doesn't change the number.
So because choice (2) mentions the scale factor is 1, this places it in the "rigid transformation" category and it's one of the four answers. Change the scale factor to anything else, and it wouldn't be an answer.
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