Question

Consider Triangle EFG with vertices E(-7, -7), F(-2,-3), and G(-1, -6). The coordinates for the new vertices E', F', and G' after a translation by (8, 3) are:

a) E'(1, -4), F'(6, 0), G'(7, -3)
b) E'(1, -10), F'(6, -6), G'(7, -9)
c) E'(1, -4), F'(6, -6), G'(7, -9)
d) E'(1, -10), F'(6, 0), G'(7, -3)

Answer 1

The new vertices after translating Triangle EFG by (8, 3) are E'(1, -4), F'(6, 0), and G'(7, -3), by adding the translation vector to the original vertex coordinates.

Step-by-step explanation:

The student inquired about the coordinates of the vertices E', F', and G' after Triangle EFG undergoes a translation by (8, 3). To find these new vertices, we add the translation vector to each of the original coordinates.

• For E(-7, -7), E' would be E + (8, 3) = (-7 + 8, -7 + 3) = (1, -4)
• For F(-2, -3), F' would be F + (8, 3) = (-2 + 8, -3 + 3) = (6, 0)
• For G(-1, -6), G' would be G + (8, 3) = (-1 + 8, -6 + 3) = (7, -3)

Therefore, the correct answer with the new vertices after translation is E'(1, -4), F'(6, 0), and G'(7, -3).