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Find the ratio in which the line segment joining the points (4,8,10) and (6,10,-8) is divided by the XZ plane.

Asked by Topperlearning User 20th February 2015, 3:17 PM
Answered by Expert
Answer:

l e t space X Z space p l a n e space d i v i d e space t h e space l i n e space s e g m e n t space j o i n i n g space A left parenthesis 6 comma 10 comma negative 8 right parenthesis space a n d space B left parenthesis 4 comma 8 comma 10 right parenthesis space i n space t h e
r a t i o space o f space k colon 1.
T h e n space t h e space c o o r d i n a t e s space o f space P space a r e
open parentheses fraction numerator 4 k plus 6 over denominator k plus 1 end fraction comma space fraction numerator 8 k plus 10 over denominator k plus 1 end fraction comma space fraction numerator 10 k minus 8 over denominator k plus 1 end fraction close parentheses
S i n c e space P space l i e s space o n space t h e space X Z space p l a n e comma space i t s space y space c o o r d i n a t e space i s space z e r o comma space i. e.
fraction numerator 8 k plus 10 over denominator k plus 1 end fraction equals 0
rightwards double arrow k equals negative 5 over 4
T h e space n e g a t i v e space s i g n space i n d i c a t e s space e x t e r n a l space d i v i s i o n.
T h e space X Z space p l a n e space d i v i d e s space A B space i n space t h e space r a t i o space o f space 5 colon 4 space e x t e r n a l l y.

Answered by Expert 20th February 2015, 5:17 PM
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