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Find the units of displacement of the point (4,2) to get the image of (7,7). Chapter (transformation) (coordinates) (translation). Please answer my questions correctly. Unnecessary answers will be reported.

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Ashraf82

Answer:

The units of the displacement are (3, 5) → T (x + 3, y + 5)

Step-by-step explanation:

The rules of translation of a point

  • If the point (x, y) is translated h units to the right and k units up, then its image is (x + h, y + k)
  • If the point (x, y) is translated h units to the right and k units down, then its image is (x + h, y - k)
  • If the point (x, y) is translated h units to the left and k units up, then its image is (x - h, y + k)
  • If the point (x, y) is translated h units to the left and k units down, then its image is (x - h, y - k)

∵ Point (4, 2) is translated by (h, k)

∵ Its image is (7, 7)

∴ The x-coordinate of the point is increased from 4 to 7

∴ The point is translated to the right by h units

∵ 4 + h = 7

∴ h = 7 - 4 = 3

∴ The point is translated to the right 3 units

∵ The y-coordinate of the point is increased from 2 to 7

∴ The point is translated up by k units

∵ 2 + k = 7

∴ k = 7 - 2 = 5

∴ The point is translated up 5 units

∴ The point is translated 3 units right and 5 units up

∴ The units of the displacement are (3, 5) → T (x + 3, y + 5)

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