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
H
I
J
K
L
3 units to the left. Which of the following would be a vertex in the translated figure?

(1 point)
Responses

(−6, 6)
(
−
6
,

6
)
left parenthesis negative 6 comma 6 right parenthesis

(−1, −2)
(
−
1
,

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

(2, 4)
(
2
,

4
)
left parenthesis 2 comma 4 right parenthesis

(−7, 4)

Answer 1

To translate the vertices of the pentagon \( HIJKL \) 3 units to the left, we need to subtract 3 from the x-coordinate of each vertex.

The original vertices of the pentagon are:

• \( H(-3, 6) \)
• \( I(-1, 4) \)
• \( J(-1, 1) \)
• \( K(-4, 1) \)
• \( L(-5, 4) \)

Now, we will translate each vertex by subtracting 3 from the x-coordinate:

1. For \( H(-3, 6) \): \[ H' = (-3 - 3, 6) = (-6, 6) \]

2. For \( I(-1, 4) \): \[ I' = (-1 - 3, 4) = (-4, 4) \]

3. For \( J(-1, 1) \): \[ J' = (-1 - 3, 1) = (-4, 1) \]

4. For \( K(-4, 1) \): \[ K' = (-4 - 3, 1) = (-7, 1) \]

5. For \( L(-5, 4) \): \[ L' = (-5 - 3, 4) = (-8, 4) \]

The vertices of the translated figure \( H'I'J'K'L' \) are now:

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

Among the options provided, the vertex \( (-6, 6) \) is one of the vertices of the translated figure.

Thus, the correct response is: \[ \boxed{(-6, 6)} \]