Question

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

Answer 1

Answer:

$K' = (\frac{1}{4} ,0)$

$L' = (\frac{1}{4} ,1)$

$M' = (\frac{5}{4} ,1)$

$N' = (\frac{5}{4} ,0)$

Step-by-step 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;

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

$K' = \frac{1}{4} * (1,0)$

$K' = (\frac{1}{4} * 1,\frac{1}{4}*0)$

$K' = (\frac{1}{4} ,0)$

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

$L' = \frac{1}{4} * (1,4)$

$L' = (\frac{1}{4} * 1,\frac{1}{4}*4)$

$L' = (\frac{1}{4} ,1)$

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

$M' = \frac{1}{4} * (5,4)$

$M' = (\frac{1}{4} * 5,\frac{1}{4}*4)$

$M' = (\frac{5}{4} ,1)$

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

$N' = \frac{1}{4} * (5,0)$

$N' = (\frac{1}{4} * 5,\frac{1}{4}*0)$

$N' = (\frac{5}{4} ,0)$

Hence, the coordinates of the dilated figure are:

$K' = (\frac{1}{4} ,0)$

$L' = (\frac{1}{4} ,1)$

$M' = (\frac{5}{4} ,1)$

$N' = (\frac{5}{4} ,0)$