What are the coordinates of the image of the point ( – 3 , 6 ) after a dilation with a center of ( 0 , 0 ) and scale factor of 1 3 ?

What are the coordinates of the image of the point (–3,6) after a dilation with a center of (0,0) and scale factor of 1/3 ?

Expert Solution

The idea of dilation, scaling, or "resizing", is to make something either bigger or smaller, but when doing this to a shape, you would have to somehow "scale" each coordinate.

Another thing is that we're not sure how the object would "move"; when scaling to make something bigger, the area/volume becomes larger, but that would mean the distances between points should become longer, so, which point goes where? A similar question arises when scaling to make things smaller.

An answer to that would be to set a "center of dilation", where all lengths are transformed in a way that makes their new distances from this center proportional to their old distances from this center.

Luckily, the dilation being centered at the origin (0,0) makes this simpler: we simply multiply the scale factor to the x and y -coordinates to obtain the image point coordinates.

1 /3 ⋅ ( - 3 , 6 )

= ( 1/ 3 ⋅ - 3 , 1/ 3 ⋅ 6 )

= (-3/ 3 , 6 /3 )

= ( - 1 , 2 )

(-1,2)

Nipun Maity answered 2 years ago

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