Page 34 - Math Course 2 (Book 2)

Solids in Space

Reflections in Space
Your Turn!
Examples Translating a Solid

1
Dilate the prism by a scale factor of . Graph the Suppose a warehouse has a room on the ground
floor that is 20 feet wide, 25 feet long, and 12 feet
image under the dilation. 2 tall. If the height of each floor is 12 feet, find the
1
Multiply each coordinate by . coordinates of each vertex of the rectangular prism
2 that represents a room in the basement of the
warehouse directly below the given room.
1 1 1
(x, y, z) → ( x, y, z)
2 2 2 A. (0, 0, 0); (0, 20, 0); (25, 20, 0); (25, 0, 0); (0, 0, 12);
(0, 20, 12); (25, 20, 12); (25, 0, 12)

B. (–12, 0, 0); (–12, 20, 0); (13, 20, 0); (13, 0, 0);
(–12, 0, 12); (–12, 20, 12); (13, 20, 12); (13, 0, 12)

C. (0, –12, 0); (0, 8, 0); (25, 8, 0); (25, –12, 0);
(0, –12, 12); (0, 8, 12); (25, 8, 12); (25, –12, 12)

D. (0, 0, –12); (0, 20, –12); (25, 20, –12); (25, 0, –12);
(0, 0, 0); (0, 20, 0); (25, 20, 0); (25, 0, 0)

A(0, 0, 0) → A′(0, 0, 0)
B(0, 4, 0) → B′(0, 2, 0)
C(2, 4, 0) → C′(1, 2, 0)
D(2, 0, 0) → D′(1, 0, 0)
E(2, 0, 2) → E′(1, 0, 1)
F(0, 0, 2) → F′(0, 0, 1) Answer
G(0, 4, 2) → G′(0, 2, 1)
H(2, 4, 2) → H′(1, 2, 1)
Reflections in Space

A sphere has a center point at P(–6, 5, 8) and a
radius of length 3 inches. If this sphere were
reflected in the yz-plane, find the coordinates of the
image of P.

A. (–6, 5, –8)
B. (–6, –5, 8)
C. (6, 5, 8)
D. (–3, 5, 8)

Plot the coordinates of the vertices of the image.

The coordinates of the
vertices are A′ (0, 0, 0), B′ (0,
Answer 2, 0), C′ (1, 2, 0), D′ (1, 0, 0),
E′ (1, 0, 1), F′ (0, 0, 1), G′ (0, 2, Answer
1),and H′ (1, 2, 1).

26