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!
I think the answer is one of them. BOOM, MIND BLOWN!
Answer:
2
Step-by-step explanation:

Answer:
y= -x+7, b= sqrt(2P/a), c=3P^2-b
Step-by-step explanation:
First, make a table regarding both of the equations. You will eventually find out that both lines intersect at the point (2, 5) after you find the points on the table. From there, subtract x from both sides in the equation x + y = 2. You will get y = -x + 2. Since they said the line was parallel, find a line that has the slope of negative one. Since we know that this line intersects the point in which the first two lines intersect, we know that the y-intercept will be 7. The equation of the line would be y=-x+7.
Multiply both sides by 2. Then, divide both sides by a to get b^2=(2P/a). Take the square root to get the value of b, which is sqrt(2P/a).
Square both sides of the equation to get P^2=(b+c)/3. Cross multiply to get 3P^2=b+c. Subtract b from both sides to get c=3P^2-b.