The line joining points A(6, 9) and B(−6, −4) are given(a) In which ratio does origin divide AB? And what it is called for AB?(b) In which ratio does the point P(2, 3) divide AB ?(c) In which ratio does the point Q(−2, −3) divide AB?(d) In how many equal parts is AB divided by P and Q?(e) What do we call P and Q for AB?
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
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