Question

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.

Answer 1

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

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)