Question

Use the image to answer the question.

An illustration of a coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A pentagon upper H upper I upper J upper K upper L is plotted on the graph with the vertices marked as closed points. The vertices of the pentagon upper H upper I upper J upper K upper L are marked at upper H left parenthesis negative 3 comma 6 right parenthesis, upper I left parenthesis negative 1 comma 4 right parenthesis, upper J left parenthesis negative 1 comma 1 right parenthesis, upper K left parenthesis negative 4 comma 1 right parenthesis, and upper L left parenthesis negative 5 comma 4 right parenthesis.

Translate the figure HIJKL
3 units to the left. Which of the following would be a vertex in the translated figure?

(1 point)
Responses

(−1, −2)
left parenthesis negative 1 comma negative 2 right parenthesis

(−6, 6)
left parenthesis negative 6 comma 6 right parenthesis

(2, 4)
left parenthesis 2 comma 4 right parenthesis

(−7, 4)
left parenthesis negative 7 comma 4 right parenthesis
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Answers

Answered by GPT-4o mini
To translate the pentagon \( HIJKL \) 3 units to the left, we need to subtract 3 from the x-coordinates of each vertex.

The original vertices are:
- \( H(-3, 6) \)
- \( I(-1, 4) \)
- \( J(-1, 1) \)
- \( K(-4, 1) \)
- \( L(-5, 4) \)

Now, we will subtract 3 from the x-coordinates:
- \( H(-3 - 3, 6) = H(-6, 6) \)
- \( I(-1 - 3, 4) = I(-4, 4) \)
- \( J(-1 - 3, 1) = J(-4, 1) \)
- \( K(-4 - 3, 1) = K(-7, 1) \)
- \( L(-5 - 3, 4) = L(-8, 4) \)

The translated vertices will be:
- \( H(-6, 6) \)
- \( I(-4, 4) \)
- \( J(-4, 1) \)
- \( K(-7, 1) \)
- \( L(-8, 4) \)

Now, let's check the given response options:
1. \( (-1, -2) \)
2. \( (-6, 6) \)
3. \( (2, 4) \)
4. \( (-7, 4) \)

Among the given options, \( (-6, 6) \) is a vertex in the translated figure.

**Answer: (-6, 6)**
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