Question

examples
perform the dilation.

1. k = 3

(-1, 13) → (_,_)
(22, 13) → (_,_)

1. k = 3/2

(-2, 4) → (_,_)
(-12, 6) → (_,_)
exercises
perform the dilation.

1. k = 1/3

(-12, 3) → (_,_)
(6, 33) → (_,_)

1. k = 4

(-12, 3) → (_,_)
(2, -3) → (_,_)

1. k = 2/7

(-21, 49) → (_,_)
(2, 35) → (_,_)

1. k = 2

(-1, 3) → (_,_)
(2, 3) → (_,_)

1. k = 2/3

(27, 9) → (_,_)
(-6, 36) → (_,_)

1. k = 4/9

(-18, 27) → (_,_)
(27, 45) → (_,_)

1. describe how to perform a dilation in your own words. use 1 - 2 complete sentences.

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ and a scale - factor $k$, the dilated point is $(kx,ky)$.

Step2: Solve for each part of the first problem ($k = \frac{1}{3}$)

For the point $(-12,3)$:
$kx=\frac{1}{3}\times(-12)= - 4$
$ky=\frac{1}{3}\times3 = 1$
For the point $(6,33)$:
$kx=\frac{1}{3}\times6 = 2$
$ky=\frac{1}{3}\times33 = 11$

Step3: Solve for each part of the second problem ($k = 4$)

For the point $(-12,3)$:
$kx=4\times(-12)=-48$
$ky=4\times3 = 12$
For the point $(2,-3)$:
$kx=4\times2 = 8$
$ky=4\times(-3)=-12$

Step4: Solve for each part of the third problem ($k=\frac{2}{7}$)

For the point $(-21,49)$:
$kx=\frac{2}{7}\times(-21)=-6$
$ky=\frac{2}{7}\times49 = 14$
For the point $(2,35)$:
$kx=\frac{2}{7}\times2=\frac{4}{7}$
$ky=\frac{2}{7}\times35 = 10$

Step5: Solve for each part of the fourth problem ($k = 2$)

For the point $(-1,3)$:
$kx=2\times(-1)=-2$
$ky=2\times3 = 6$
For the point $(2,3)$:
$kx=2\times2 = 4$
$ky=2\times3 = 6$

Step6: Solve for each part of the fifth problem ($k=\frac{2}{3}$)

For the point $(27,9)$:
$kx=\frac{2}{3}\times27 = 18$
$ky=\frac{2}{3}\times9 = 6$
For the point $(-6,36)$:
$kx=\frac{2}{3}\times(-6)=-4$
$ky=\frac{2}{3}\times36 = 24$

Step7: Solve for each part of the sixth problem ($k=\frac{4}{9}$)

For the point $(-18,27)$:
$kx=\frac{4}{9}\times(-18)=-8$
$ky=\frac{4}{9}\times27 = 12$
For the point $(27,45)$:
$kx=\frac{4}{9}\times27 = 12$
$ky=\frac{4}{9}\times45 = 20$

Step8: Answer for problem 7

To perform a dilation, multiply the $x$ - coordinate and $y$ - coordinate of each point by the scale - factor $k$.

Answer:

1. $(-12,3)\to(-4,1)$; $(6,33)\to(2,11)$
2. $(-12,3)\to(-48,12)$; $(2,-3)\to(8,-12)$
3. $(-21,49)\to(-6,14)$; $(2,35)\to(\frac{4}{7},10)$
4. $(-1,3)\to(-2,6)$; $(2,3)\to(4,6)$
5. $(27,9)\to(18,6)$; $(-6,36)\to(-4,24)$
6. $(-18,27)\to(-8,12)$; $(27,45)\to(12,20)$
7. To perform a dilation, multiply the $x$ - coordinate and $y$ - coordinate of each point by the scale - factor $k$.