What is dilation with a scale factor of 2 ?

First, it is important to remember the definition of Dilation.

A Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure, before the transformation) have the same shape, but their sizes are different.

In this case, you know that the triangle ABC is dilated by a scale factor of 2 with a center of dilation at the origin.

According to the exercise, point C has these coordinates:

c(2,1)

Therefore, in order to find the coordinates of C', you need to multiply the coordinates of point C by scale factor 2.

Then, you get that the coordinates of the point C' are:

c=(2*2,1*2)

c=(4,2)