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

(−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

(−1, −2)

Answer 1

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

Here are the original coordinates of the vertices:

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

Now let's translate each vertex:

• H: (-3 - 3, 6) = (-6, 6)
• I: (-1 - 3, 4) = (-4, 4)
• J: (-1 - 3, 1) = (-4, 1)
• K: (-4 - 3, 1) = (-7, 1)
• L: (-5 - 3, 4) = (-8, 4)

Now reviewing the translated vertices, we find:

• The new vertex for H is (-6, 6).
• The new vertex for I is (-4, 4).
• The new vertex for J is (-4, 1).
• The new vertex for K is (-7, 1).
• The new vertex for L is (-8, 4).

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

Therefore, the correct response is:

(−6, 6)