Answer
\( 2 \) feet
Work Step by Step
To find the length of the image of the pole on the projection plane, we can use similar triangles.
Let's denote:
- \( L \) as the length of the pole,
- \( d \) as the distance from the center of projection to the projection plane,
- \( x \) as the distance from the center of projection to one end of the pole,
- \( y \) as the distance from the point where the line intersects the projection plane to the edge of the image of the pole.
From the information given, we have:
- \( L = 8 \) feet (the length of the pole),
- \( x = 4 \) feet (the distance from the center of projection to one end of the pole),
- \( d = 1 \) foot (the distance from the center of projection to the projection plane),
- \( y = ? \) (the distance from the point where the line intersects the projection plane to the edge of the image of the pole).
Since the pole is parallel to the projection plane, we have similar triangles. Therefore, we can set up the proportion:
\[
\frac{y}{d} = \frac{L}{x}
\]
Substituting the given values:
\[
\frac{y}{1} = \frac{8}{4}
\]
Solving for \( y \):
\[
y = \frac{8 \times 1}{4} = 2 \text{ feet}
\]
