5.1 Determine the new coordinates of the dot above if it is shifted ten units down and six units to the right. 1.5.2 The new coordinates of the corners of the triangle if is reflected about the x-axis

The dot is located at $(-8, 8)$.

Shifting ten units down means subtracting 10 from the y-coordinate: $8 - 10 = -2$.
Shifting six units to the right means adding 6 to the x-coordinate: $-8 + 6 = -2$.

The new coordinates of the dot are $\boxed{\text{(-2, -2)}}$.

1.5.2 The new coordinates of the corners of the triangle if it is reflected about the x-axis.

The vertices are at $(2, 8)$, $(6, 8)$, and $(4, 12)$.

When a point $(x, y)$ is reflected about the x-axis, its new coordinates become $(x, -y)$.
For $(2, 8)$, the new coordinates are $(2, -8)$.
For $(6, 8)$, the new coordinates are $(6, -8)$.
For $(4, 12)$, the new coordinates are $(4, -12)$.

The new coordinates of the corners of the triangle are $\boxed{\text{(2, -8), (6, -8), and (4, -12)}}$.