Page 30 - Math Course 2 (Book 2)

Solids in Space
Mo. 7

Lesson 6 Key Concept

Distance Formula in Space
KEY CONCEPTS:
1. Graph solids in space. Given two points A(x ,y , z ) and B(x ,y , z ) in
2
2
1
1
2
1
2. Use the Distance and Midpoint Formulas space, the distance between and B is given by the
for points in space following equation.
3. Translate a solid to find the coordinates of
each vertex. d = 2 2 2
4. Find the coordinates of an image as (x – x ) + (y – y ) + (z – z )
1
2
2
1
2
1
reflected in space.
MO. 7 - L6a z
Graph Solids in Space B(x ,y , z )
2 2 2
Vocabulary A-Z

Let us learn some vocabulary
0 y
A(x ,y , z )
1
1
1
ordered triple x
A point in space is represented by an ordered triple
of real numbers (x, y, z).

In the figure at the right, the ordered triple (2, 3, 6) Midpoint Formula in Space
locates point P. Notice that a rectangular prism is
used to show perspective.
Given two points A(x ,y , z ) and B(x ,y , z ) in
1 1 1 2 2 2
space, the midpoint of AB is at
z
x + x 2 + y y + z z 2
1
,
1
1
2
,
P(2, 3, 6) 2 2 2
6 units
z
A(x , y , z )
1 1 1
y = 3
M x
0 y
O
x = 2
y
B(x , y , z )
x 2 2 2

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