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Translation how many units right followed by a dilation with a scale factor of?

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Translation How Many Units Right Followed By A Dilation With A Scale Factor Of Help Please class=

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Answers:

Translation  1   unit to the right.

Followed by a dilation with scale factor   2  

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Explanation:

The ultimate goal is to somehow turn the smaller blue triangle (ABC) into the green triangle (XYZ).

This means that we want to do three things:

  • Move point A to X
  • Move point B to Y
  • Move point C to Z

This works because any triangle is uniquely defined by the three corner points.

Let's focus on point C. Right now, it is located at (1,1). If we move it 3 units to the right, then it arrives at (4,1). We have the correct x coordinate, but the y coordinate is not correct. We're one unit below our target, which is where Z is located.

But what we could do is instead of moving 3 units to the right, we can move 1 unit to the right. Point C will go from (1,1) to (2,1). Now apply a dilation with scale factor 2. This will multiply the coordinates by 2. So (2,1) doubles to (4,2) which is exactly where point Z is located. This process is effectively trial and error, so we got a bit lucky and didn't have to do much work to move C to Z.

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We'll do the same steps for points A and B to see if we can get them to move to X and Y respectively.

  • Point A is located at (2,3). Shifting one unit to the right lands us on (3,3). Double the coordinates to get to (6,6). This is where point X is located.
  • Point B is at (3,1). It moves to (4,1) after shifting one unit to the right. Then it moves to (8,2) when we double the coordinates, and this is where point Y is located.

So the process of "shift one unit to the right, double the coordinates" works for points A and B also.

Keep in mind that the order of the transformations is important. We cannot double the coordinates first, and then shift one unit to the right. If we did that, then point C would move to (3,2) which is not where point Z is located.

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