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?

Answer 1

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

Let's calculate the new coordinates for each vertex:

- Vertex H(-3, 6):
New H = (-3 - 3, 6) = (-6, 6)

- Vertex I(-1, 4):
New I = (-1 - 3, 4) = (-4, 4)

- Vertex J(-1, 1):
New J = (-1 - 3, 1) = (-4, 1)

- Vertex K(-4, 1):
New K = (-4 - 3, 1) = (-7, 1)

- Vertex L(-5, 4):
New L = (-5 - 3, 4) = (-8, 4)

Therefore, the new vertices after the translation would be:

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

So, any of these new coordinates (like (-6, 6) or (-4, 4)) would be a vertex in the translated figure.

If you need to choose a specific vertex, you can choose one from the calculated set. For example, one such vertex of the translated figure would be H'(-6, 6).