Answer:
The rule that describes the translation of ΔABC to ΔA'B'C' is
(x, y) → (x + 4, y + 3) ⇒ b
Step-by-step explanation:
Let us revise the rule of translation of a point
- The image of the point (x, y) after translation h units to the right and k units up is (x + h, y + k)
- The image of the point (x, y) after translation h units to the right and k units down is (x + h, y - k)
- The image of the point (x, y) after translation h units to the left and k units up is (x - h, y + k)
- The image of the point (x, y) after translation h units to the left and k units down is (x - h, y - k)
Let us solve the question
∵ Point A = (-3, 0)
∵ Point A' = (1, 3)
→ Subtract the x-coordinate of A from the x-coordinate of A' to find h
∵ h = 1 - - 3 = 1 + 3 = 4
→ h is a positive value, then the translation is to the right
∴ Point A translated 4 units to the right
→ Subtract the y-coordinate of A from the y-coordinate of A' to find k
∵ k = 3 - 0 = 3
→ K is a positive value, then the translation is up
∴ Point A translated 3 units up
∴ The rule of translation is (x, y) → (x + 4, y + 3)
Let us find B' and C' using the rule of translation
∵ B = (-3, -2)
∵ The rule of translation is (x, y) → (x + 4, y + 3)
∴ B' = (-3 + 4, -2 + 3)
∴ B' = (1, 1) ⇒ same as the figure
∵ C = (-1, -2)
∵ The rule of translation is (x, y) → (x + 4, y + 3)
∴ B' = (-1 + 4, -2 + 3)
∴ B' = (3, 1) ⇒ same as the figure
The rule that describes the translation of ΔABC to ΔA'B'C' is
(x, y) → (x + 4, y + 3)
