Question

Transformations & Congruence (you can plot all 3 houses on the SAME coordinate plane)

Chapter 1:

You are just beginning your life as an adult and have bought a house in a new housing development.

Your house is located at A (2,2), B (4,2), C (4,4), D (3,5), and E (2,4).

Question 1

Plot the points where your house is located, in your favorite color. Name this color here as the color of the original location.



Chapter 2:

A flood moves your house exactly 4 blocks to the left and 2 blocks down.



Question 2

Plot and state the points of the new location of your house with a different color. Name the new color you use on your graph here. (x,y) for all 5 points (x,y) (x,y) (x,y) (x,y) (x,y)



Question 3

Describe specifically the formal transformation (write the translation using arrow notation (x +/- ?, y +/- ? ) that occurred when the flood moved your house.



Question 4

Is your new house after this transformation congruent to the original house? Explain your answer.



Chapter 3:

You have become an internet sensation after your video received over 5 million views in one week. This made you 1 million dollars. You call a builder and ask them to build you a house twice the size of your current house.



Question 5

Plot the points of the new house after a scale factor of 2 (applied to house in Question 2)with the given coordinates . (This is a transformation called dilation.) Use a different color to plot the points. Name the color you use on your graph here. The new coordinates of your house after the scale factor is applied are?? (x,y) (x,y) (x,y) (x,y) (x,y)



Question 6

Is your new house after this transformation congruent to the house in Chapter 2? Or is it an enlargement or reduction?? Explain your answer.

Answer 1

Chapter 1 — original house
- Color used: blue (original location)
- Original points:
A (2, 2)
B (4, 2)
C (4, 4)
D (3, 5)
E (2, 4)

Chapter 2 — after the flood (translation 4 left, 2 down)
- Color used: red (new location)
- Translation in arrow notation: (x, y) → (x − 4, y − 2)
- New points (apply (x−4, y−2) to each original point):
A → A1 (2−4, 2−2) = (−2, 0)
B → B1 (4−4, 2−2) = (0, 0)
C → C1 (4−4, 4−2) = (0, 2)
D → D1 (3−4, 5−2) = (−1, 3)
E → E1 (2−4, 4−2) = (−2, 2)

Question 4 — congruence after translation
- Yes. A translation preserves size and shape, so the new house (after the flood) is congruent to the original house.

Chapter 3 — dilation (scale factor 2) applied to the house from Chapter 2
- Color used: green (dilated/enlarged house)
- Dilation rule (about the origin): (x, y) → (2x, 2y)
- New points (double each Chapter 2 point):
A1 → A2 (2·(−2), 2·0) = (−4, 0)
B1 → B2 (2·0, 2·0) = (0, 0)
C1 → C2 (2·0, 2·2) = (0, 4)
D1 → D2 (2·(−1), 2·3) = (−2, 6)
E1 → E2 (2·(−2), 2·2) = (−4, 4)

Question 6 — congruence or enlargement/reduction
- The dilated house is an enlargement (scale factor 2). It is not congruent to the Chapter 2 house because all lengths are doubled; shapes are similar but not the same size, so not congruent.