Answer:
Step-by-step explanation:
Step 1: What are the couch's original coordinates?
- A: (-4, 2)
- N: (-4, 3)
- G: (-1, 3)
- L: (-1, 4)
- E: (-5, 4)
- S: (-5, 2)
Step 2: Rotate the couch 90° counterclockwise.
Rule: (x, y) → (-y, x)
- A': (-4, 2) → (-2, -4)
- N': (-4, 3) → (-3, -4)
- G': (-1, 3) → (-3, -1)
- L': (-1, 4) → (-4, -1)
- E': (-5, 4) → (-4, -5)
- S': (-5, 2) → (-2, -5)
Step 3: Now reflect the "new" couch over the y-axis.
Rule: (x, y) → (-x, y)
- A'': (-2, -4) → (2, -4)
- N'': (-3, -4) → (3, -4)
- G'': (-3, -1) → (3, -1)
- L'': (-4, -1) → (4, -1)
- E'': (-4, -5) → (4, -5)
- S'': (-2, -5) → (2, -5)
Step 4: Finally translate the new new" couch right 1 unit and up 5 units.
Rule: (x + 1, y + 5)
- A''': (2, -4) → (2 + 1, -4 + 5) → (3, 1)
- N''': (3, -4) → (3 + 1, -4 + 5) → (4, 1)
- G''': (3, -1) → (3 + 1, -1 + 5) → (4, 4)
- L''': (4, -1) → (4 + 1, -1 + 5) → (5, 4)
- E''': (4, -5) → (4 + 1, -5 + 5) → (5, 0)
- S''': (2, -5) → (2 + 1, -5 + 5) → (3, 0)
Step 5: Use the distance formula to show that the length of EG is the same as the length of E'''G'''.
- EG: (-5, 4)(-1, 3)
- E'''G''': (5, 0)(4, 4)
Distance between E(-5, 4) and G(-1, 3)
- x₁ = -5
- x₂ = -1
- y₁ = 4
- y₂ = 3

Distance between E'''(5, 0) and G'''(4, 4)

This means that the length of EG is the same as the length of E'''G'''.
Hope this helps!
okey
you needed the sum or division?
Answer:
1st one
Step-by-step explanation: