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)
(−7, 4)
(2, 4)
(−6, 6)
To translate the figure HIJKL 3 units to the left, we need to subtract 3 from the x-coordinate of each vertex.
Given the vertices of the original figure HIJKL are:
H: (x, y)
I: (x, y)
J: (x, y)
K: (x, y)
L: (x, y)
To translate the figure 3 units to the left, we subtract 3 from the x-coordinate of each vertex:
H': (x-3, y)
I': (x-3, y)
J': (x-3, y)
K': (x-3, y)
L': (x-3, y)
Now we compare the translated vertices with the given options:
(−1, −2): This point is not one of the translated vertices.
(−7, 4): This point is not one of the translated vertices.
(2, 4): This point is not one of the translated vertices.
(−6, 6): This point is one of the translated vertices. It matches the vertex K'.
Therefore, the correct answer is (−6, 6).
To translate a figure 3 units to the left, we subtract 3 from the x-coordinates of all the vertices.
The x-coordinate of vertex H is -1 - 3 = -4.
The x-coordinate of vertex I is -7 - 3 = -10.
The x-coordinate of vertex J is 2 - 3 = -1.
The x-coordinate of vertex K is -6 - 3 = -9.
The x-coordinate of vertex L is -6 - 3 = -9.
Therefore, the vertex in the translated figure is (-10, y), where y is the y-coordinate of vertex I.
Among the given options, the vertex (-7, 4) is the only one with x-coordinate -10. Therefore, the answer is (−7, 4).