a triangle is dilated by a scale factor of 1/2 centered at the origin the dilated figures then translated for units right and three units down which transformation rule represents this function

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30-10-2022
Mathematics

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a triangle is dilated by a scale factor of 1/2 centered at the origin the dilated figures then translated for units right and three units down which transformation rule represents this function

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MaeveW212424 MaeveW212424 · Answer 1 · 2022-10-30T05:31:59+01:00

We want to determine the formula of the whole transformation. To do so, we will find the transformation step by step.

First, we are told that there is a dilation by a scale of 1/2 (or by a scale of 0.5, which is equivalent). We achieve this by multiplying each coordinate by the dilation factor. We leads to the formula

[tex](x,y)\to(0.5x,0.5y)[/tex]

Now, we will shift this formula 4 units right. Since it is a horizontal shift, it affects the first coordinate only. In this case, moving 4 units right means adding 4 to the first coordinate. This leads to the formula

[tex](0.5x,0.5y)\to(0.5x+4,0.5y)[/tex]

Finally, we shift everything 3 units down. We do so by subtracting 3 from the second coordinate. This leads to the formula

[tex](0.5x+4,0.5y)\to(0.5x+4,0.5y-3)[/tex]