Answer:
To find the coordinates of the vertices of the triangular prism, we need to consider the base triangle and the height of the prism.
Given:
- The legs of the triangular base are 4 inches and 5 inches.
- The height of the prism is 4 inches.
Let's start by finding the coordinates of the vertices of the triangular base. Since the legs of the base triangle are 4 inches and 5 inches, we can assume that the base triangle is a right triangle with one leg parallel to the x-axis and the other leg parallel to the y-axis.
Let's label the vertices of the base triangle as A, B, and C.
Vertex A: (0, 0) - This will be the origin.
Vertex B: (4, 0) - This vertex lies on the x-axis and is 4 inches away from the origin.
Vertex C: (0, 5) - This vertex lies on the y-axis and is 5 inches away from the origin.
Now, let's find the coordinates of the vertices of the top triangle. Since the height of the prism is 4 inches, the top triangle will be a translation of the base triangle 4 units along the z-axis.
Vertex A': (0, 0, 4)
Vertex B': (4, 0, 4)
Vertex C': (0, 5, 4)
Therefore, the coordinates of the vertices of the triangular prism are:
A (0, 0, 0)
B (4, 0, 0)
C (0, 5, 0)
A' (0, 0, 4)
B' (4, 0, 4)
C' (0, 5, 4)
