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.

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)