Q. 25.0( 3 Votes )
A point C with z-
Answer :
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)
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