Question

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

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

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

(−6, 6)

Answer 1

To translate the pentagon HIJKL 3 units to the left, we will 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 apply the translation to each vertex:

1. H(-3, 6) → H'(-3 - 3, 6) = H'(-6, 6)
2. I(-1, 4) → I'(-1 - 3, 4) = I'(-4, 4)
3. J(-1, 1) → J'(-1 - 3, 1) = J'(-4, 1)
4. K(-4, 1) → K'(-4 - 3, 1) = K'(-7, 1)
5. L(-5, 4) → L'(-5 - 3, 4) = L'(-8, 4)

Now, we can analyze the options provided:

1. (−1, −2)
2. (−7, 4)
3. (2, 4)
4. (−6, 6)

From our translations, we see that the translated point H' is (-6, 6) which matches one of the response options.

Thus, the correct answer is: (−6, 6).