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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)

(-7, 4)

(-1, -2)

(2, 4)

1 answer

To translate the pentagon HIJKL 3 units to the left, we subtract 3 from the x-coordinate of each vertex. Let's calculate the new coordinates for each vertex:

  1. Vertex H \((-3, 6)\): \[ (-3 - 3, 6) = (-6, 6) \]

  2. Vertex I \((-1, 4)\): \[ (-1 - 3, 4) = (-4, 4) \]

  3. Vertex J \((-1, 1)\): \[ (-1 - 3, 1) = (-4, 1) \]

  4. Vertex K \((-4, 1)\): \[ (-4 - 3, 1) = (-7, 1) \]

  5. Vertex L \((-5, 4)\): \[ (-5 - 3, 4) = (-8, 4) \]

Now, the new vertices of the translated pentagon HIJKL are:

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

From the provided options, the vertex that appears in the translated figure is:

\((-6, 6)\)

Therefore, the answer is \((-6, 6)\).