A point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10). Find the coordinates.

Given: A point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10)

To find: the coordinates of C

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 C(x, y, 8), and C divides AB in ratio k: 1

Therefore, m = k and n = 1

A(2, -3, 4) and B(8, 0, 10)

Coordinates of C using section formula:

On comparing:

⇒ 10k + 4 = 8(k + 1)

⇒ 10k + 4 = 8k + 8

⇒ 10k – 8k = 8 – 4

⇒ 2k = 4

⇒ k = 2

Here C divides AB in ratio 2:1

⇒ x = 6

⇒ y = -1

Hence, Coordinates of C are (6, -1, 8)