Answer:
The translation is (5, -6)
Step-by-step explanation:
- If the point (x, y) translated h unit right and k unit up, then its image is (x + h, y + k) and the translation is (h, k)
- If the point (x, y) translated h unit left and k unit up, then its image is (x - h, y + k) and the translation is (-h, k)
- If the point (x, y) translated h unit right and k unit down, then its image is (x + h, y - k) and the translation is (h, -k)
- If the point (x, y) translated h unit left and k unit down, then its image is (x - h, y - k) and the translation is (-h, -k)
Let us solve the question
∵ The coordinates of point Q are (4, 5)
∴ x = 4 and y = 5
∵ The coordinates of point Q' are (9, -1)
∴ x' = 9 and y' = -1
→ That means x increased and y decreased ⇒ 3rd case above
∴ The point Q is moved to the right and down
→ By using the 3rd rule above ⇒ (x + h, y - k)
∵ x + h = 9
∵ x = 4
→ Substitute x by 4
∴ 4 + h = 9
→ Subtract 4 from both sides
∵ 4 - 4 + h = 9 - 4
∴ h = 5
∵ y - k = -1
∵ y = 5
→ Substitute y by 5
∴ 5 - k = -1
→ Subtract 5 from both sides
∵ 5 - 5 - k = -1 - 5
∴ -k = -6
→ Divide both sides by -1
∴ k = 6
∵ The translation is (h, -k) in the 3rd case
∵ h = 5 and k = 6
∴ The translation is (5, -6)
We can check the rule by finding D' the image of the point D
∵ D = (-5, -2)
∵ D' = (x + h, y - k)
∵ D' = (-5 + 5, -2 - 6)
∴ D' = (0, -8) as the given point D'
∴ The translation is correct
