Graph the image of rectangle PQRS after dilation with a scale factor of 1/4, centered at the origin.

Question

My daughter has a sheet on dilation and Scale factors and I have no clue how to help her. Some Please Help me.

How do you know How to work out prolem to draw on the graph

Answer 1

A dilation of the rectangle PQRS will produce an image that is the same shape as rectangle PQRS but a different size. In this case the size is smaller since the scale factor is less than 1.

 

The center of the dilation is a fixed point.

 

The notation for dilation is D_k where k is the scale factor.

 

For a dilation centered around the origin

 

D_k (x,y) = (kx, ky)

 

So let's say you have a rectangle PQRS where

P = (0,0)

Q = (4,0)

R = (4,4)

S = (0,4)

 

To get the dilation of this PQRS to P'Q'R'S' with scale factor 1/4

you multiply every coordinate by 1/4. 

 

P' = (0.0)

Q' = (1,0)

R' = (1,1)

S' = (0,1)

 

You can plot both these rectangles to see they are same shape but second is smaller than original

and they both are centered on origin.