Given: Points P(4, 2, -6) and Q(10, -16, 6)
To find: the coordinates of points which trisect the line PQ
Formula used:
Section Formula: A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).
The coordinates of C is given by,
\(\Big(\frac{nx+ma}{m+n},\frac{ny+mb}{m+n},\frac{nz+mc}{m+n}\Big)\)
Let Point R(x, y, z) and Point S(a, b, c) trisects line PQ
So, PR : RS : SQ = 1 : 1 : 1
Now, we will firstly apply section formula on PQ and find coordinates of R
Therefore, m = 1 and n = 2
P(4, 2, -6) and Q(10, -16, 6)
Coordinates of R using section formula:
Now, we will apply section formula on PQ and find coordinates of S
Therefore, m = 2 and n = 1
P(4, 2, -6) and Q(10, -16, 6)
Coordinates of R using section formula:
Hence, Coordinates of R and S are (6, -4, -2) and (8, -10, 2) respectively
