Question

dilations project
cameron burton
directions
step 1: draw/trace any logo or picture on graph 1.
step 2: on graph 1, pick at least 8 points to label with letters a, b, c, and so on.
step 3: choose a scale factor to dilate by. (choose ½, 2 or 3)
step 4: fill out the table with the pre - image and image coordinates.
step 5: draw the dilated image on graph 2.
step 6: answer the analysis questions.
graph 1 (with a grid and a drawn apple - like figure)
my scale factor: r =
pre - image coordinates | image coordinates
a (3, 3) | a (6, 6)
b (7, 3) | b (14, 6)
c (7, 7) | c (14, 14)
d (3, 7) | d (6, 14)
e (5, 3) | e (10, 6)
f (7, 5) | f (14, 10)
g (5, 7) | g (10, 14)
h (3, 5) | h (6, 10)
i (, ) | i (, )
j (, ) | j (, )
k (, ) | k (, )
l (, ) | l (, )
m (, ) | m (, )
n (, ) | n (, )
analysis questions

1. imagine a student was given the dilation that you made. would they be able to use the coordinates to find the scale factor? explain.
2. there are 2 pieces of information you can use to determine whether a dilation is a reduction or an enlargement. what type of dilation did you make, and what are the 2 ways a student could determine the dilation you made?

Explanation:

Step1: Choose Scale Factor

Let's choose a scale factor \( r = 2 \). This means we will multiply each coordinate of the pre - image by 2 to get the image coordinates.

Step2: Calculate Image Coordinates for A

Pre - image A: \( (3,3) \). Using the dilation formula \( (x',y')=(r\times x,r\times y) \) with \( r = 2 \), we have \( x'=2\times3 = 6 \) and \( y'=2\times3=6 \). So \( A'=(6,6) \).

Step3: Calculate Image Coordinates for B

Pre - image B: \( (7,3) \). Then \( x' = 2\times7=14 \) and \( y'=2\times3 = 6 \). So \( B'=(14,6) \).

Step4: Calculate Image Coordinates for C

Pre - image C: \( (7,7) \). Then \( x'=2\times7 = 14 \) and \( y'=2\times7=14 \). So \( C'=(14,14) \).

Step5: Calculate Image Coordinates for D

Pre - image D: \( (3,7) \). Then \( x'=2\times3 = 6 \) and \( y'=2\times7 = 14 \). So \( D'=(6,14) \).

Step6: Calculate Image Coordinates for E

Pre - image E: \( (5,3) \). Then \( x'=2\times5=10 \) and \( y'=2\times3 = 6 \). So \( E'=(10,6) \).

Step7: Calculate Image Coordinates for F

Pre - image F: \( (7,5) \). Then \( x'=2\times7 = 14 \) and \( y'=2\times5=10 \). So \( F'=(14,10) \).

Step8: Calculate Image Coordinates for G

Pre - image G: \( (5,7) \). Then \( x'=2\times5 = 10 \) and \( y'=2\times7=14 \). So \( G'=(10,14) \).

Step9: Calculate Image Coordinates for H

Pre - image H: \( (3,5) \). Then \( x'=2\times3=6 \) and \( y'=2\times5 = 10 \). So \( H'=(6,10) \).

Answer:

For the table:

• \( A'=(6,6) \)
• \( B'=(14,6) \)
• \( C'=(14,14) \)
• \( D'=(6,14) \)
• \( E'=(10,6) \)
• \( F'=(14,10) \)
• \( G'=(10,14) \)
• \( H'=(6,10) \)

For the scale factor, if we used the above calculations, \( r = 2 \) (enlargement, since \( r>1 \)).