Page 32 - Math Course 2 (Book 2)

Solids in Space

Distance and Midpoint Formulas in Space Distance and Midpoint Formulas in Space

Examples A. Determine the distance between A(0, –5, 0) and
B(1, –2, –3).

A. √19
Determine the distance between F(4, 0, 0) and
G(–2, 3, –1). B. √7

Distance C. √59
2
2
FG = (x – x ) + (y – y ) + (z – z ) 2 Formula in
2 1 2 1 2 1 Space
D. 3 √2
2
= [4–(–2)] + (0–3) + [0–(–1)] 2 Substitution
2
= 46 Simplify.
Answer

Answer √46
Determine the midpoint M of AB.

3
1
3
Determine the midpoint M of FG. A. ( , – , – )
2
2
2
3
7
1
x + x y + y Z + Z Midpoint B. ( , – , – )
2
2
2
M = ( 1 2 , 1 2 , 1 2 ) Formula in
3
1
5
2 2 2 Space C. ( , – , )
4 + (–2) 0 + 3 0 + (–1) 2 2 2
= ( , , ) Substitution 1 7 3
2 2 2 D. ( – , – , – )
2
2
2
3 1
= ( 1, , – ) Simplify
2
2
3 1
Answer ( 1, , – )
2
2
Your Turn!
Graph a Rectangular Solid
In the following diagram, what is the correct
ordered triple for Point N?
A. (2, 1, –3)
B. (1, 2 –3)
C. (2, –3, 1)
D. (1, –3, 2)

Answer

24