Question

The triangle with the vertices

(4, 5, 1), (0, 8, 2), (4, 7, 8)
is translated five units to the right along the y-axis. Determine the coordinates of the translated triangle. (Give your vertices in the same order as the original vertices.)
(x, y, z) =
(x, y, z) =
(x, y, z) =

Answer 1

The translated triangle's vertices, after moving five units to the right along the y-axis, are (4, 10, 1), (0, 13, 2), and (4, 12, 8).

Step-by-step explanation:

The student was asked to determine the coordinates of a triangle translated five units to the right along the y-axis. To do this, we apply a translation vector that affects only the y-coordinate of each vertex. Since the translation is along the y-axis by five units, each y-coordinate of the original vertices is increased by 5.

Original vertices:

• (4, 5, 1)
• (0, 8, 2)
• (4, 7, 8)

Applying the translation to each y-coordinate:

• (4, 5 + 5, 1) = (4, 10, 1)
• (0, 8 + 5, 2) = (0, 13, 2)
• (4, 7 + 5, 8) = (4, 12, 8)

The coordinates of the translated triangle are therefore:

(4, 10, 1), (0, 13, 2), (4, 12, 8).