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

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

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

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

(−1, −2)

Answer 1

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

The original vertices are:

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

Now, applying the translation:

• 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)

The new vertices after translation are:

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

Now let's check the response options given: (−7, 4) → Not a vertex (2, 4) → Not a vertex (−6, 6) → This is a vertex (H') (−1, −2) → Not a vertex

Thus, the correct answer is: (−6, 6)