Find the ratio in which the line segment joining the points (2, 4, 5) and (3, -5, 4) is divided by the yz-plane.

Given: points A(2, 4, 5) and B(3, -5, 4)


To find: the ratio in which the line joining given points is divided by the yz-plane


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,



the x coordinate is always 0 on yz-plane


Let Point C(0, y, z), and C divides AB in ratio k: 1


Therefore, m = k and n = 1


A(2, 4, 5) and B(3, -5, 4)



Coordinates of C using section formula:




On comparing:



3k + 2 = 0(k + 1)


3k + 2 = 0


3k = –2



Hence, C divides AB externally in ratio 2 : 3


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