Question

perspective drawings recall from the text, that a perspective drawing is drawn using vanishing points.
a. does the drawing at the right represent a perspective drawing?
explain why or why not.
b. using heavy dashed lines, draw the
hidden lines of the prism.
c. redraw the prism so that it uses
two vanishing points.

Explanation:

Part (a)

A perspective drawing uses vanishing points, and this drawing has lines that appear to converge towards a single vanishing point (the apex of the triangular - like part of the prism's top), which is consistent with the definition of a perspective drawing (using vanishing points to create the illusion of depth).

Part (b)

(Note: Since this is a drawing - based task, the following is a description of how to draw the hidden lines. In a prism (a type of polyhedron with two congruent polygonal bases connected by rectangular faces), for the given prism (which seems to be a combination of a rectangular prism and a pyramid - like top, but focusing on the prism part), the hidden lines would be the edges that are not visible from the current perspective. For a rectangular prism - like part, if we consider the back - facing edges that are obscured by the front - facing faces, we would draw dashed lines for:

1. The vertical edge at the back of the right - hand side of the rectangular base (if the front right vertical edge is visible, the back right vertical edge is hidden).
2. The horizontal edges at the back of the top and bottom faces of the rectangular part that are not visible.

To actually draw them, we would identify the edges that are behind the visible faces and draw them with heavy dashed lines. For example, in the rectangular prism portion, the edges that are on the far side (opposite to the viewer) and are covered by the front faces should be drawn as dashed lines.

Part (c)

(Note: To redraw the prism with two vanishing points (this is a two - point perspective drawing), follow these steps:

1. Set up the vanishing points: Draw a horizontal line (the horizon line) and mark two points on it, \(V_1\) and \(V_2\), which will be the two vanishing points.
2. Draw the front - facing edge: Draw a vertical line (representing the front - most vertical edge of the prism) at a suitable position on the paper, below the horizon line.
3. Draw the lines to the vanishing points: From the top and bottom endpoints of this vertical line, draw lines to \(V_1\) and \(V_2\) respectively.
4. Define the depth: Decide on the depth of the prism. To do this, we can pick a point along the line from the top of the vertical edge to \(V_1\) (or \(V_2\)) and from the bottom of the vertical edge to \(V_1\) (or \(V_2\)) to represent the back - facing vertical edges. Then, draw lines between these new points (connecting the points on the lines to \(V_1\) and \(V_2\)) to form the back - facing edges of the prism, ensuring that the shape remains a prism (with two congruent polygonal bases, in this case, rectangles).

The final redrawn prism will have its horizontal edges (parallel to the length and width of the base) converging towards the two different vanishing points on the horizon line, creating a more realistic two - point perspective view of the prism.)

Answer:

Yes, the drawing represents a perspective drawing.