Q. 25.0( 3 Votes )

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.

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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