Question

I need help with it pls

Answer 1

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 = $√((x_2-x_1)^2+(y_2-y_1)^2)$}\\\\\large \textsf {d = $√((-1-(-5))^2+(3-4)^2)$}\\\\\large \textsf {d = $√((-1+5)^2+(3-4)^2)$}\\\\\large \textsf {d = $√(4^2+(-1)^2)$}\\\\\ \large \textsf {d = $√(16+1)$}\\\\\large \textsf {d = $√(17)$}\\\\\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 = $√((x_2-x_1)^2+(y_2-y_1)^2)$}\\\\\large \textsf {d = $√((4-5)^2+(4-0)^2)$}\\\\\large \textsf {d = $√((-1)^2+4^2)$}\\\\\large \textsf {d = $√(1+16)$}\\\\\ \large \textsf {d = $√(17)$}\\\\ \large \textsf {d = ${4.12}$}`

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

Hope this helps!