Find the coordinates of the points which trisect the line segment joining the points P(4, 2, -6) and Q(10, -16, 6).

Question

Philoid · Accepted Answer

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,

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