Dianela0802idn
Answered

IDNLearn.com is designed to help you find accurate answers with ease. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

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)​

Sagot :

Ashraf82idn

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

Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.