Question

Find the image of (4, 5) under S0.5 withcenter at (1, 6)

Answer 1

We have a pre-image that is the point (4, 5).

We applied a dilation with scale 0.5 and center at (1, 6).

As the center is not the center of coordinates, we applied a change of coordinates to make (1, 6) the center of coordinates.

Then, the point (4, 5) becomes:

`(4,5)\longrightarrow(4-1,5-6)=(3,-1)`

We apply the dilation to the point and get:

`(3,-1)\longrightarrow(0.5\cdot3,0.5\cdot(-1))=(1.5,-0.5)`

Now, we go back to the original coordinates:

`(1.5,-0.5)\longrightarrow(1.5+1,-0.5+6)=(2.5,5.5)`

We can verify the transformation in a graph:

The graph makes sense, as the image point is half the distance from the center of dilation that the pre-image point.