Question

Which rule describes the composition of transformations that maps ABC to A"B"C"?

Answer 1

Answer:

The rule describes the composition of transformations that maps Δ ABC to Δ A"B"C" is rx-axis, T(x - 6, y - 2) ⇒ B

Step-by-step explanation:

Let us revise some rules of transformation

• If the point (x, y) reflected across the x-axis, then its image is (x, -y), the rule of reflection is rx-axis (x, y) → (x, -y)

• If The point (x, y) reflected across the y-axis, then its image is (-x, y), the rule of reflection is ry-axis (x, y) → (-x, y)

• If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)

• If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)

• If the point (x, y) translated vertically up by k units then its image is (x, y + k)→ (x + h, y) ⇒ T (x, y) → (x, y + k)

• If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)

Look at the graph and list the vertice of each triangle

∵ A = (5, -5) and A' = (5, 5)

∵ B = (1, -2) and B' = (1, 2)

∵ C = (1, -5) and C' = (1, 5)

→ The signs of y-coordinates of all vertices of ΔABC are opposite

   in ΔA'B'C'

∴ Δ ABC is reflected across the x-axis

∴ The rule is rx-axis (x, y) → (x, -y)

∵ A' = (5, 5) and A" = (-1, 3)

∵ -1 - 5 = -6 and 3 - 5 = -2

∵ B' = (1, 2) and B" = (-5, 0)

∵ -5 -1 = -6 and 0 - 2 = -2

∵ C' = (1, 5) and C" = (-5,3)

∵ -5 - 1 = -6 and 3 - 5 = -2

→ That means every x-coordinate in Δ A'B'C' added by -6 and every

   y-coordinate add by -2

∴ Δ A'B'C' is translated 6 units to the left and 2 units down

∴ The rule is T (x, y) → (x - 6, y - 2)

The rule describes the composition of transformations that maps Δ ABC to Δ A"B"C" is rx-axis, T(x - 6, y - 2)