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Triangle upper A upper B upper C is plotted in quadrants 1 and 2 of a coordinate plane. Each of the vertices is labeled.

If triangle ABC
is translated horizontally by −3
and vertically by +2, which of the following options correctly depicts triangle ABC
and its image, triangle A′B′C′
? Enter the number of the correct option.

Option #1:

Triangle upper A upper B upper C and triangle upper A prime upper B prime upper C prime are plotted on a coordinate plane. Triangle upper A prime upper B prime upper C prime is shaded with dotted sides. The sides of the other triangle are solid.



Option #2:

Triangle upper A upper B upper C and triangle upper A prime upper B prime upper C prime are plotted on a coordinate plane. Triangle upper A prime upper B prime upper C prime is shaded with dotted sides. The sides of the other triangle are solid.



Option #3:

Triangle upper A upper B upper C and triangle upper A prime upper B prime upper C prime overlap on a coordinate plane. Triangle upper A prime upper B prime upper C prime is shaded with dotted sides. The sides of the other triangle are solid.

(1 point)
Option #
is correct.

1 answer

To find which option correctly depicts triangle ABC and its translated image triangle A'B'C', we first apply the transformations given:

  1. The translation is horizontal by -3 and vertical by +2.
  2. For each vertex of triangle ABC (let's say A(x, y), B(x', y'), and C(x'', y'')), the new coordinates after the translation will be:
    • A' = (x - 3, y + 2)
    • B' = (x' - 3, y' + 2)
    • C' = (x'' - 3, y'' + 2)

After translating, triangle A'B'C' will occupy a different position in the coordinate plane compared to triangle ABC.

Given the options:

  1. In options #1 and #2, triangle ABC and triangle A'B'C' are shown together with one being solid and the other being dotted. This implies they are clearly separated, indicating that A'B'C' is not overlapping with ABC.
  2. In option #3, there is overlapping of the two triangles, which is not correct because the triangles are positioned differently after the translation.

To summarize:

  • If the triangle has been translated, the original triangle (solid) and the image triangle (dotted) should appear separately, not overlapping.
  • The option that shows triangle A'B'C' with dotted lines and not overlapping with triangle ABC, which has solid lines, is correct.

Without seeing the actual figures, the choice would be based on this explanation and deductive reasoning. Typically, if they position the triangles as described, an option like option #1 or #2 would be correct while option #3 would not be correct.

Since both options #1 and #2 are very similar in description, I cannot definitively determine which specific option is correct without seeing the visuals.

If asked to select one option instead of both, you would just need to choose one of them that best depicts the separation clearly. Please follow up with the specific images to narrow down a definitive answer further.