Question

A polygon is translated 3 units to the right and 4 units down, then it’s reflected across the x-axis, and then it’s dilated by a factor of 4 with the origin as the center of dilation. Create a function modeling the transformation.

Answer 1

`(x,y)\rightarrow (4x+12,-4y+16)`

Explanation:

1 transformation - translation 3 units to the right and 4 units down. This translation has the rule

`(x,y)\rightarrow (x+3,y-4)`

2 transformation - reflection across the x-axis. This reflection has the rule

`(x,y)\rightarrow (x,-y)`

3 transformation - dilation by a factor of 4 with the origin as the center of dilation. This dilation has the rule

`(x,y)\rightarrow (4x,4y)`

Now, the sequence of these three transformation has the rule

`(x,y)\rightarrow\limits^{\text{1st transformation}} (x+3,y-4)\rightarrow\limits^{\text{2nd transformation}}(x+3,-(y-4))\rightarrow\limits^{\text{3rd transformation}} (4(x+3),4(-(y-4)))\\ \\(x,y)\rightarrow (4x+12,-4y+16)`