20 a triangle has vertices at b(−3, 0), c(2, −1), d(−1, 2). which series of transformations would produce an image with vertices b″(4, 1), c″(−1, 0), d″(2, 3)?
a) (x, y) → (x, −y), (x, y) → (x + 1, y + 1)
b) (x, y) → (−x, y), (x, y) → (x + 1, y + 1)
c) (x, y) → (x, −y), (x, y) → (x + 2, y + 2)
d) (x, y) → (−x, y), (x, y) → (x + 2, y + 2)

(x , y) → (-x , y), (x , y) → (x + 1 , y + 1) ⇒ answer B

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis  then its image is (x , -y)

- If point (x , y) reflected across the y-axis  then its image is (-x , y)

- If the point (x , y) translated horizontally to the right by h units

 then its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 then its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 then its image is (x , y - k)

* Lets solve the problem

∵ The vertices of the Δ BCD are:

# B = (-3 , 0)

# C = (2 , -1)

# D = (-1 , 2)

∵ The images of its vertices after a series of transformations are:

# B″ = (4 , 1)

# C" = (-1 , 0)

# D" = (2 , 3)

* Lets find the write answer

- (x , -y) means Δ BCD across x-axis

∴ B' = (-3 , 0)

∴ C' = (2 , 1)

∴ D' = (-1 , -2)

- (x + 1 , y + 1) means translate ΔB'C'D' 1 unit to the right and 1 unit up

∴ B" = (-2 , 1)

∴ C" = (0 , 1)

∴ D" = (3 , 4)

- Not the vertices of Δ B"C"D"

∴ Answer A is not our answer

- (-x , y) means reflect ΔBCD across y-axis

∴ B' = (3 , 0)

∴ C' = (-2 , -1)

∴ D' = (1 , 2)

- (x + 1 , y + 1) means translate ΔB'C'D' 1 unit to the right and 1 unit up

∴ B" = (4 , 1)

∴ C" = (-1 , 0)

∴ D" = (2 , 3)

- The same with the vertices of Δ B"C"D"

∴ Answer B is our answer

∴ series of transformations would produce ΔB"C"D" is

   (x , y) → (-x , y), (x , y) → (x + 1 , y + 1)

The answer the the question of which you have asked would be the second letter in the english lexicon, B.

he will have 300 because he is really broke and 300 is in his imangine

step-by-step explanation: he ehe heh step by the thy

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8