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Similar Figures in the Coordinate Plane Quick Check

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Question
Use the image to answer the question.

Triangle F G H is drawn with a solid line and is located in quadrant 2 of a coordinate plane. Triangle J K I is drawn with a dotted line and is located in quadrant 4.

Assess two figures using the definitions of transformations to determine whether the figures are similar. Is ΔFGH∼ΔIJK
, and for what reason?

(1 point)
Responses

No. If point J
was at (−6,6)
, the triangles would be similar.
No. If point upper J was at left parenthesis negative 4 comma 5 right parenthesis , the triangles would be similar.

Yes. All sides are proportional.
Yes. All sides are proportional.

Yes. All angles are congruent.
Yes. All angles are congruent.

No. If point J
was at (6,−6)
, the triangles would be similar.
No. If point upper J was at left parenthesis 4 comma negative 5 right parenthesis , the triangles would be similar.
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3 answers

To determine whether triangles ΔFGH and ΔIJK are similar, we need to analyze the criteria for similarity of triangles. Triangles are similar if:

  1. Their corresponding angles are congruent.
  2. The lengths of their corresponding sides are proportional.

If triangle FGH is drawn in quadrant 2 and triangle IJK is drawn in quadrant 4, their positions suggest they may not be similar without further information about their angles and side lengths.

Based on the given responses:

  • "No. If point J was at (−6,6), the triangles would be similar."
  • "No. If point J was at (−4,5), the triangles would be similar."
  • "Yes. All sides are proportional."
  • "Yes. All sides are proportional."
  • "Yes. All angles are congruent."
  • "No. If point J was at (6,−6), the triangles would be similar."
  • "No. If point J was at (4,−5), the triangles would be similar."

It seems that the triangles are not similar based on their current configurations, as the positions in different quadrants may affect their side lengths or angles.

If either of the responses indicating "Yes" refers to the conditions being true (all sides proportional or all angles congruent), then those triangles could be similar under the right circumstances. However, without the actual measurements or angles provided, we can't confirm that as true or apply only to these triangles in their given positions.

Considering the context of the question and typical classroom scenarios, the most appropriate answer is likely:

No. If point J was at (−6, 6), the triangles would be similar.

This indicates that for the triangles to be similar, the coordinates of triangle IJK need to be adjusted accordingly.

thank you

You're welcome! If you have any more questions or need further assistance, feel free to ask. Good luck with your studies!