nslations on the Coordinate Plane

Question

On a coordinate plane, a triangle has points D (negative 2.5, 5), E (0, negative 1), and F (negative 5, negative 1).

What is the y-coordinate of point D after a translation of (x, y) → (x + 6, y – 4)?



D′(3.5,
)

Answer 1

To find the new y-coordinate of point D after the translation described by the function \( (x, y) \rightarrow (x + 6, y - 4) \), we start with the original coordinates of point D, which are \( D(-2.5, 5) \).

1. Translate the x-coordinate: \[ x' = -2.5 + 6 = 3.5 \]

2. Translate the y-coordinate: \[ y' = 5 - 4 = 1 \]

After the translation, point D becomes \( D'(3.5, 1) \).

Thus, the y-coordinate of point D after the translation is \( 1 \).

So, you can fill in the blank:

D′(3.5, 1).