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sveticcg [70]
2 years ago
6

I need help with it pls

Mathematics
1 answer:
Basile [38]2 years ago
4 0

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

\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(-1-(-5))^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{(-1+5)^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{4^2+(-1)^2}$}\\\\\ \large \textsf {d = $\sqrt{16+1}$}\\\\\large \textsf {d = $\sqrt{17}$}\\\\\large \textsf {d = ${4.12}$}

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

  • x₁ = 5
  • x₂ = 4
  • y₁ = 0
  • y₂ = 4

\large \textsf  {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(4-5)^2+(4-0)^2}$}\\\\\large \textsf {d = $\sqrt{(-1)^2+4^2}$}\\\\\large \textsf {d = $\sqrt{1+16}$}\\\\\ \large \textsf {d = $\sqrt{17}$}\\\\ \large \textsf {d = ${4.12}$}

This means that the length of EG is the same as the length of E'''G'''.

Hope this helps!

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