Use the image to answer the question.

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

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

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

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

(−1, −2)

Answer 1

To translate the pentagon HIJKL 3 units to the left, we 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, let's calculate the new vertices after the translation:

1. H: \((-3 - 3, 6) = (-6, 6)\)

2. I: \((-1 - 3, 4) = (-4, 4)\)

3. J: \((-1 - 3, 1) = (-4, 1)\)

4. K: \((-4 - 3, 1) = (-7, 1)\)

5. L: \((-5 - 3, 4) = (-8, 4)\)

Now, the new vertices are:

• H'(-6, 6)
• I'(-4, 4)
• J'(-4, 1)
• K'(-7, 1)
• L'(-8, 4)

Among the provided options, the vertex that corresponds to the translated figure is:

• (-6, 6)

So the correct answer is \((-6, 6)\).