Solution: The dilation of gk by a scale factor of 2 centered at (-2,-4) is and
.
Explanation:
It is given that the scale factor is 2 and center of dilation is (-2,-4).
If the center of dilation is (a,b) with scale factor k, then the dilation of a point P(x,y) is determined by the given formula.
.....(1)
To find the g' substitute x=0, y=0, a=-2, b=-4 and k=2 in equation (1).
To find the k' substitute x=4, y=4, a=-2, b=-4 and k=2 in equation (1).
Therefore, the dilation of gk by a scale factor of 2 centered at (-2,-4) is and
.