Question

Q and D are points on a polygon. Q' D' are points of the polygon under a translation. Determine the translation. Write your answer as (x,y).
Q (4,5) Q' (9,-1)
D (-5,-2) D' (0,-8)​

Answer 1

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