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The graph of TUVW has coordinates T(–4, 2), U(–2, –1), V(1, 2), and W(–2, 3).

Graph TUVW and its image after a translation of 3 units right and 3 units down.

Multiple choice question.

Figures T U V W and T prime U prime V prime W prime. T prime (0, negative 1), U prime (2, negative 4), V prime (5, negative 1), W prime (2, 0).

Figures T U V W and T prime U prime V prime W prime. T prime (negative 1, 0), U prime (1, negative 3), V prime (4, 0), W prime (1, 1).

Figures T U V W and T prime U prime V prime W prime. T prime (negative 1, negative 1), U prime (1, negative 4), V prime (4, negative 1), W prime (1, 0).

Figures T U V W and T prime U prime V prime W prime. T prime (4, negative 1), U prime (1, 0), V prime (negative 1, negative 1), W prime (1, negative 4).

3 answers

To perform the translation of the figure TUVW, we will move each vertex 3 units to the right (which means adding 3 to the x-coordinates) and 3 units down (which means subtracting 3 from the y-coordinates).

Given the original coordinates:

  • T(–4, 2)
  • U(–2, –1)
  • V(1, 2)
  • W(–2, 3)

We will calculate the new coordinates after the translation:

  1. Point T(–4, 2):

    • New x-coordinate: –4 + 3 = –1
    • New y-coordinate: 2 - 3 = -1
    • New coordinates: T'(-1, -1)

  2. Point U(–2, –1):

    • New x-coordinate: –2 + 3 = 1
    • New y-coordinate: –1 - 3 = -4
    • New coordinates: U'(1, -4)

  3. Point V(1, 2):

    • New x-coordinate: 1 + 3 = 4
    • New y-coordinate: 2 - 3 = -1
    • New coordinates: V'(4, -1)

  4. Point W(–2, 3):

    • New x-coordinate: –2 + 3 = 1
    • New y-coordinate: 3 - 3 = 0
    • New coordinates: W'(1, 0)

So, the new coordinates after the translation are:

  • T'(-1, -1)
  • U'(1, -4)
  • V'(4, -1)
  • W'(1, 0)

Now we compare the calculated coordinates with the answer choices provided:

  1. First option: T' (0, -1), U' (2, -4), V' (5, -1), W' (2, 0) - Incorrect
  2. Second option: T' (-1, 0), U' (1, -3), V' (4, 0), W' (1, 1) - Incorrect
  3. Third option: T' (-1, -1), U' (1, -4), V' (4, -1), W' (1, 0) - Correct
  4. Fourth option: T' (4, -1), U' (1, 0), V' (-1, -1), W' (1, -4) - Incorrect

The correct answer is the third option: T' (-1, -1), U' (1, -4), V' (4, -1), W' (1, 0).

Write the coordinates of the image.



T’(
,
)



U’(
,
)



V’(
,
)



W’(
,
)

The coordinates of the image after the translation are as follows:

  • T’(-1, -1)
  • U’(1, -4)
  • V’(4, -1)
  • W’(1, 0)

So, you can fill it out like this:

T’(-1, -1)

U’(1, -4)

V’(4, -1)

W’(1, 0)