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Use the image to answer the question. Translate triangle ABC by 3 units to the left and 5 units down. Which of the following are the coordinates of new triangle A′B′C′ ? (1 point) Responses A′(−1,2), B′(−3,−2), C′(2,0) upper A prime left parenthesis negative 1 comma 2 right parenthesis , upper B prime left parenthesis negative 3 comma negative 2 right parenthesis , upper C prime left parenthesis 2 comma 0 right parenthesis A′(1,0), B′(−1,−4), C′(4,−2) upper A prime left parenthesis 1 comma 0 right parenthesis , upper B prime left parenthesis negative 1 comma negative 4 right parenthesis , upper C prime left parenthesis 4 comma negative 2 right parenthesis A′(1,10), B′(−1,6), C′(4,7) upper A prime left parenthesis 1 comma 10 right parenthesis , upper B prime left parenthesis negative 1 comma 6 right parenthesis , upper C prime left parenthesis 4 comma 7 right parenthesis A′(7,0), B′(5,−4), C′(10,−2)

5 answers

To find the new coordinates of triangle A′B′C′ after translating triangle ABC by 3 units to the left and 5 units down, we need to apply these transformations to the original coordinates of points A, B, and C.

  1. Translation left by 3 units: This means we subtract 3 from the x-coordinate of each point.
  2. Translation down by 5 units: This means we subtract 5 from the y-coordinate of each point.

Let's say the original coordinates of A are (x_A, y_A), B are (x_B, y_B), and C are (x_C, y_C). After the transformations, the new coordinates A′, B′, and C′ will be:

  • A′(x_A - 3, y_A - 5)
  • B′(x_B - 3, y_B - 5)
  • C′(x_C - 3, y_C - 5)

Now, we can evaluate which set of coordinates matches after performing the translation:

  • If A is at (x_A, y_A), then the new coordinate A′ will be calculated as (x_A - 3, y_A - 5).
  • Repeat this for points B and C.

Given the options, you would need the exact coordinates of the original triangle A, B, and C to find A′, B′, and C′ after the transformation.

Since the original coordinates are not provided, I cannot determine the selected answer without that information. However, once you calculate A′, B′, and C′ using the above transformation on the coordinates of triangle ABC, you can compare the results with the options provided to select the correct one. Please provide the original coordinates of triangle ABC to derive the translated coordinates.

Use the image to answer the question. What kind of translation has been made to triangle ABC ? (1 point) Responses Triangle ABC has been translated 3 units to the right and 7 units down. Triangle upper A upper B upper C has been translated 3 units to the right and 7 units down. Triangle ABC has been translated 2 units to the right and 7 units down. Triangle upper A upper B upper C has been translated 2 units to the right and 7 units down. Triangle ABC has been translated 3 units to the left and 7 units up. Triangle upper A upper B upper C has been translated 3 units to the left and 7 units up. Triangle ABC has been translated 3 units to the right and 6 units down.

To determine the translation made to triangle ABC, we need to know the original coordinates of triangle ABC and the coordinates of the translated triangle A′B′C′.

Since I do not have access to the image required to visually determine the translation or the coordinates of the triangle before and after translation, I cannot definitively identify the translation from the provided options.

However, the translation is generally described by how much the triangle has moved along the x-axis (right or left) and the y-axis (up or down).

  1. Moving to the right means adding to the x-coordinate, while moving to the left means subtracting from the x-coordinate.
  2. Moving up means adding to the y-coordinate, while moving down means subtracting from the y-coordinate.

Given the options:

  1. Translated 3 units to the right and 7 units down.
  2. Translated 3 units to the right and 7 units down. (Duplicate option)
  3. Translated 2 units to the right and 7 units down.
  4. Translated 2 units to the right and 7 units down. (Duplicate option)
  5. Translated 3 units to the left and 7 units up.
  6. Translated 3 units to the left and 7 units up. (Duplicate option)
  7. Translated 3 units to the right and 6 units down.

To choose the correct option, you would need to check the original and new coordinates of the triangle in the image.

Please provide the original coordinates and those of the translated triangle, or describe the changes in positions of the triangle, and I could help you determine the correct translation statement.

If coordinates (−2,−5) undergo a translation vector of <2,−3> in the coordinate plane, what would the resulting coordinates be?(1 point) Responses (0,−8) left parenthesis 0 comma negative 8 right parenthesis (4,−2) left parenthesis 4 comma negative 2 right parenthesis (4,2) left parenthesis 4 comma 2 right parenthesis (0,−2)

To find the resulting coordinates after applying the translation vector \( \langle 2, -3 \rangle \) to the point \((-2, -5)\), we perform the following calculations:

  1. Add the x-component of the translation to the x-coordinate:
    \( -2 + 2 = 0 \)

  2. Add the y-component of the translation to the y-coordinate:
    \( -5 - 3 = -8 \)

So, the new coordinates after the translation are:

\[ (0, -8) \]

Therefore, the resulting coordinates are \((0, -8)\).

Thus, the correct response is:

\[ (0, -8) \]