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? (−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)
left parenthesis negative 1 comma negative 2 right parenthesis

Answer 1

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

The original coordinates of the vertices are:
- H(-3, 6)
- I(-1, 4)
- J(-1, 1)
- K(-4, 1)
- L(-5, 4)

Now, we'll translate each vertex:

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

Now let's list the translated vertices:
- H'(-6, 6)
- I'(-4, 4)
- J'(-4, 1)
- K'(-7, 1)
- L'(-8, 4)

Now, we can check the options given:

1. **(-6, 6)**: This is a vertex of the translated figure (H').
2. **(2, 4)**: This point does not match any of the new vertices.
3. **(-7, 4)**: This point does not match any of the new vertices.
4. **(-1, -2)**: This point does not match any of the new vertices.

The corresponding vertex after translation is **(-6, 6)**.