Page 33 - Math Course 2 (Book 2)

Solids in Space

MO. 7 - L6b Solve
Coordinates of Translated
coordinates
Finding the Coordinates of the vertices, (x, y, z + 10 )
(x, y, z)
Vertices Preimage image

A (0, 0, 0) A’ (0, 0, 10)
Let’s Begin B (0, 9, 0) B’ (0, 9, 10)

C (6, 9, 0) C’ (6, 9, 10)

Translating a Solid D (6, 0, 0) D’ (6, 0, 10)
E (0, 0, 8) E’ (0, 0, 18)
Examples F (0, 9, 8) F’ (0, 0, 18)

G (6, 9, 8) G’ (6, 8, 18)
ARCHITECTURE
Suppose a two-story home has a bathroom on H (6, 0, 8) H’ (6, 0, 18)
the first floor that is 9 feet wide, 6 feet deep, and
8 feet tall. Likewise, a bathroom on the second Check Check that the distance between
floor, directly above the one on the first floor, has corresponding vertices is 10 feet.
the same dimensions. If the second floor is 10
feet above the first floor, find the coordinates of
each vertex of the rectangular prism that
represents the second-floor bathroom.

Explore Since the bathroom is a rectangular
prism, use positive values for x, y, and (0, 0, 10); (0, 9, 10); (6, 9, 10);
z. Write the coordinates of each corner. Answer (6, 0, 10); (0, 0, 18); (0, 9, 18);
The points of the bathroom will rise 10 (6, 9, 18); (6, 0, 18)
feet for the points of the second-floor
bathroom.
Plan Use a translation equation (x, y, z)→(x, y,
z + 10) to find the coordinates of each
vertex of the rectangular prism that
represents the second-floor bathroom

25