Question

The coordinates of the endpoints of EF

are E(-4, 4) and F(-2, 1) . After a translation, the coordinates of the endpoints of the image of

EF are E' (, 1) and F'(6, -2). What translation was performed on EF


?


Responses

Pick the answer below.

Pick the answer below.

Answer 1

To find the translation that was performed on the segment EF with endpoints E(-4, 4) and F(-2, 1) to obtain the endpoints E'(x, 1) and F'(6, -2), we need to determine the translation vector.

First, let's calculate the translation needed for point E to move to E':

1. The x-coordinate of E is -4, and the x-coordinate of E' is unknown, but the y-coordinate of E' is 1.
We can calculate the translation in the y-direction:
- The translation in the y-direction from E(4) to E'(1) is:
\[
\Delta y_E = 1 - 4 = -3
\]
So E moves down by 3 units.

Next, let's move on to point F:

2. The x-coordinate of F is -2, and the x-coordinate of F' is 6. Similarly, we compute the translation for F:
- The translation in the x-direction from F(-2) to F'(6) is:
\[
\Delta x_F = 6 - (-2) = 6 + 2 = 8
\]
F moves right by 8 units.
- The translation in the y-direction from F(1) to F'(-2) is:
\[
\Delta y_F = -2 - 1 = -3
\]
So F also moves down by 3 units.

Now, we can summarize the complete translation:

- The translation vector is \( (8, -3) \).

Thus, the translation that was performed on EF is:
**Translate right by 8 units and down by 3 units.**