the line joining points A(6,9)and B(-6,-9) are given
Answers
Answer:
1:1
Origin is mid point of AB
1:2
2:1
AP = PQ = QB = AB/3
Step-by-step explanation:
correct data :
The line joining points A(6, 9) and B(−6, −9)
origin divides in ratio m : n
using formula
(x , y) = (mx₂ + nx₁)/(m +n) , (my₂ + ny₁)/(m +n)
AP = PQ = QB = AB/3
0 = (-6m + 6n)/(m + n) => 6m = 6n => m = n => m/n = 1:1
or 0 = (-9m + 9n)/(m + n) => 9m = 9n => m = n => m/n = 1:1
Origin is mid point of AB
the point P(2, 3) divide AB
=> 2 = (-6m + 6n)/(m + n) & 3 = (-9m + 9n)/(m + n)
=> 2m + 2n = -6m + 6n or 3m + 3n = -9m + 9n
=> 8m = 4n => 12m = 6n
=> m/n = 1 : 2 => m/n = 1 : 2
the point Q(−2, −3) divide AB
=> => -2 = (-6m + 6n)/(m + n) & 3 = (-9m + 9n)/(m + n)
=> -2m - 2n = -6m + 6n or -3m - 3n = -9m + 9n
=> 4m = 8n => 6m = 12n
=> m/n = 2 : 1 => m/n = 2 : 1
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