The points O, A, B, X and Y are such that OA = a, OB = b, OX = 3a and OY = 3b. Find BX and AY in terms of a and b. Further, if the point P divides AY in the ratio 1:3, then express BP in terms of a and b.
Answers
Given : The points O, A, B, X and Y are such that OA = a, OB = b, OX = 3a and OY = 3b . the point P divides AY in the ratio 1:3
To find : BX and AY in terms of a and b.
express BP in terms of a and b.
Solution:
OX = 3a
OB = b
BX = OX - OB = 3a - b
BX = 3a - b
OY = 3b
OA = a
AY = OY - OA = 3b - a
AY = 3b - a
P divides AY in the ratio 1:3
AP = (1/4)(3b- a)
PY = (3/4)(3b - a)
AB = OB - OA = b - a
BP = | AP - AB |
= | (1/4)(3b- a) - (b - a) |
= | (3b - a - 4b + 4a ) /4 |
= | | (3a - b) / 4 |
BP = ( 3a - b)/4 or ( b - 3a ) /4
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