Ratio is used to find the coordinates of a point P which divides the segment joining the points A ,B and C internally or externally in the ratio m : n.
Formulae: |
| Coordinate that divide the segment externally, |
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Example:
Find the coordinate of the line joining the point (3,4,5) and (6,7,8) that divide the line segment externally in the ratio of 3:4.
m=3,n=4,x1=3,y1=4,z1=5 and x2=6, y2=7,z2=8
(3*6 -4 * 3)/(3-4),(3*7 -4 *4)/(3-4),(3*8-4*5)/(3-4)
(18 -12)/(-1),(21 -16)/(-1),(24-20)/(-1)
(-6,-5,-4)
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| Coordinate that divide the segment internally, |
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Example:
Find the coordinate of the line joining the point (3,4,5) and (6,7,8), that divide the line segment internally in the ratio of 3:4.
m=3,n=4,x1=3,y1=4,z1=5 and x2=6, y2=7,z2=8
(3*6 +4 * 3)/(3+4),(3 *7 +4 *4)/(3+4),(3*8+4*5)/(3+4)
(18 +12)/(7),(21 +16)/(7),(24+20)/7
(30/7,37/7,44/7
(4.3,5.3,6.3)
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