Question

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

Answer 1

To dilate a triangle by a scale factor of 1/2 and then translate it, multiply the original coordinates by the scale factor and add the translation amounts.

Step-by-step explanation:

To dilate a triangle by a scale factor of 1/2 centered at the origin, you need to multiply the coordinates of each vertex by the scale factor. If the original triangle has vertices A(x1, y1), B(x2, y2), and C(x3, y3), the new vertices are A'(1/2x1, 1/2y1), B'(1/2x2, 1/2y2), and C'(1/2x3, 1/2y3).

Next, to translate the dilated triangle four units right and three units down, you simply add the translation amounts to the x and y-coordinates of each vertex. The new vertices are A''(1/2x1 + 4, 1/2y1 - 3), B''(1/2x2 + 4, 1/2y2 - 3), and C''(1/2x3 + 4, 1/2y3 - 3).

Answer 2

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

`(x,y)\to(0.5x,0.5y)`

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

`(0.5x,0.5y)\to(0.5x+4,0.5y)`

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

`(0.5x+4,0.5y)\to(0.5x+4,0.5y-3)`