Question

What are the coordinates of the image of L for a dilation with center (0,0) and scale factor 1/4?

Answer 1

`K' = ((1)/(4) ,0)`

`L' = ((1)/(4) ,1)`

`M' = ((5)/(4) ,1)`

`N' = ((5)/(4) ,0)`

Explanation:

Given

K(1,0)

L(1,4)

M(5,4)

N(5,0)

Scale Factor = 1/4

Dilation with center (0,0)

Required

New coordinates of the quadrilateral

To get the new coordinates, we simply multiply the scale factor with each coordinate;

This is done as follows;

`If\ K =(1,0),\ then;`

`K' = (1)/(4) * (1,0)`

`K' = ((1)/(4) * 1,(1)/(4)*0)`

`K' = ((1)/(4) ,0)`

`If\ L =(1,4),\ then`

`L' = (1)/(4) * (1,4)`

`L' = ((1)/(4) * 1,(1)/(4)*4)`

`L' = ((1)/(4) ,1)`

`If\ M =(5,4),\ then`

`M' = (1)/(4) * (5,4)`

`M' = ((1)/(4) * 5,(1)/(4)*4)`

`M' = ((5)/(4) ,1)`

`If\ N =(5,0),\ then`

`N' = (1)/(4) * (5,0)`

`N' = ((1)/(4) * 5,(1)/(4)*0)`

`N' = ((5)/(4) ,0)`

Hence, the coordinates of the dilated figure are:

`K' = ((1)/(4) ,0)`

`L' = ((1)/(4) ,1)`

`M' = ((5)/(4) ,1)`

`N' = ((5)/(4) ,0)`