Question

EFG has vertices E(1, 5), F(0, -3), and G(-1, 2). EFG is translated along the vector (7,1), and the image is reflected across the x-axis. What are the coordinates of the final image of G?

a) G'(6, -3)
b) G'(0, 3)
c) G'(-8, -1)
d) G'(-6, 3)

Answer 1

The coordinates of the final image of G, based on the translation and reflection, would be a) G'(6, -3)

How to translate the image ?

For the translation, add 7 to the x-coordinate and 1 to the y-coordinate of each point of the triangle EFG.

Then the reflection changes the sign of the y-coordinate of each point (the x-coordinate remains the same).

Translation:

Original coordinates of G: (-1, 2)

Translation vector: (7, 1)

New coordinates after translation: G' = (-1 + 7, 2 + 1)

= (6, 3)

Reflection across the x-axis:

Coordinates after translation: G'(6, 3)

After reflection, y-coordinate changes sign:

G'' = (6, -3)

In conclusion, the coordinates of the final image of G after the translation and reflection are (6, -3).