determine the rotio in which the stringt line x-y-2=0 divide the line segment joining the points (3 -1) and (8 9)
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rakshit233:
find the ratio in which the point (-3 p) divides the line segment joing the point (-5 4) and (-2 3) and find the value of p
Can u help
(-5,4),(-3,p),(-2,3)are collinear.( - 3+5)/(-3+2)=(p-4)/(p-3) then P=10/3.let (-3,p) divides the line joining (-5,4)and (-2,3)in the ratio k:1,then (-2k-5)/k+1=-3. then k=2.hence the ratio is 2:1.
the value of the p
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K I had not seen sorry
tq a lot
from which place u are ?
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Hey there!
Question:
In what ratio does the line x-y-2=0 divide the line segment joining the points A (3, -1) and B (8, 9)?
Answer:
Let the ratio be k:1.
And, point of intersection be (X,Y).
Now,
X = (m₁x₂ + m₂x₁) /( m₁ + m₂)
X = (k*8 + 1*3) / (k+1)
X = (8k + 3) /( k + 1)
And,
Y = (m₁y₂ + m₂y₁) /( m₁ + m₂)
Y = ( k* 9 - 1*1) / (k+1)
Y = (9k-1)/(k+1)
Now,
Since, the point (X,Y) also lies on x - y - 2 = 0.
So, it will satisfy the given equation,
x - y - 2 = 0.
(8k+3)/(k+1) - (9k-1)/(k+1) - 2 = 0
⇒ (8k + 3 - 9k - 1)/ (k+1) = 2
⇒ -k +4 = 2k + 2
⇒ 4 = 2k+ k + 2
⇒2 = 3k
⇒ 2/3 = k
or, k = 2 / 3
Now,
Ratio = k : 1 = (2 / 3) : 1 = 2 : 3
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