If triangle abc is defined by the coordinates a(-4, -4), b(2, -2), c(0, 4) is dilated by a scale factor of 1 2 , with resulting vertex a' at (-2, -2). what is the center of the dilation?

  the origin, (0, 0)

Step-by-step explanation:

The coordinates of A' are 1/2 those of A, meaning each has been multiplied by the scale factor 1/2. When the dilated points are all the original points multiplied by the scale factor, the center of dilation is the origin.

For center of dilation Q, the image of a point A after dilation by a factor of k is ...

  A' = kA + (k-1)Q

Then for points A, A', and dilation factor k, the center of dilation can be found to be ...

  (A' -kA)/(k-1) = Q

Here, that is ...

  Q = ((-2, -2) -(1/2)(-4, -4))/(1/2 -1) = (0, 0)/(-1/2)

  Q = (0, 0)

a. the residual plot for model 1 has a random pattern and is a good fit for the data.

answer: when you burn wood, the carbon reacts with the oxygen in the air to create ash and smoke. that is a permanent change you cannot undo that.

step-by-step explanation: