9514 1404 393
Answer:
see attached
Step-by-step explanation:
Each point moves to the same distance on the other side of the mirror line. The slope of the mirror line is 1, so the points move along a line perpendicular to that, one with a slope of -1. You can make sure the distances are the same by counting the grid squares.
Answer:
Step-by-step explanation:
T is a linear transformation, hence it is homogeneous (T(cr)=cT(r) for all real c and r∈ℝ³) and additive (T(r+s)=T(r)+T(s), for all r,s∈ℝ³). Apply these properties with r=3u and s=2v to obtain:
We don't have an explicit definition of T, so it's more difficult to compute T(3u+2v) directly without using these properties.
Given :
Center of sphere , C( 1 , -1 , 6 ) .
To Find :
Find equations of the spheres with center (1, −1, 6) that touch the following planes.a) xy-plane b) yz-plane c) xz-plane .
Solution :
a)
Distance of the point from xy-plane is :
d = 6 units .
So , equation of circle with center C and radius 6 units is :
b)
Distance of point from yz-plane is :
d = 1 unit .
So , equation of circle with center C and radius 1 units is :
c)
Distance of point from xz-plane is :
d = 1 unit .
So , equation of circle with center C and radius 1 units is :
Hence , this is the required solution .