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

(−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)**