求A = (4,4,16)對平面:x+y+z=21的對稱點
(A) (-2,-2,-2)
(B) (2,2,14)
(C) (6,6,30)
(D) (-6,-6,-18)
TT
正確答案:(B)
r
M
•A'
Assume that A' is the symmetric point of A in the above diagram.
First, we computer,
which is the line that passes through A and is perpendicular to π:
x 4 y 4
Z-
- 16
r:
=
=
1
1
Then, solving the following three simultaneous equations from r and π :
x y = 0, x z = −12, x + y + z = 21
we find the intersection point M of r and π
M = (3,3,15)
Since M is the midpoint of AA', we have
A-M
A'
= M - A'
= 2M - A
=2(3,3,15)-(4,4,16)
= (2,2,14).
