The ratio in which the point p(3/4, 5/12) divides the segmet joining the points A (1/2, 3/4) and B ( 2,-5) is:
Answers
Correction: The ratio in which the point P(3/4, 5/12) divides the segment joining the points A(1/2, 3/2) and B (2, -5) is:
We've been given points A(1/2, 3/2) and B(2, -5), which when joined, are divided by the point P(2, -5).
We have to find the ratio in which the P(2, -5) divides AB. We can find the ratio using the Section formula.
Also:
Where m₁ : m₂ is the ratio in which the line is divided.
Here:
x₁ = 1/2
x₂ = 2
y₁ = 3/4
y₂ = -5
We know that the x-coordinate of P(3/4, 5/12) which is 3/4, is equal to (2m₁ + (m₂/2))/(m₁ + m₂).
Similarly the y-coordinate, which is 5/12, is equal to (-5m₁ + (3m₂/2))/(m₁ + m₂).
Now, Let us equate 5/12, with (-5m₁ + (3m₂/2))/(m₁ + m₂).
Transposing 2 to the other side we get:
Therefore, the line AB is divided in the ratio 1:5 by the point P(3/4, 5/12).