If : 1 is the ratio in which the line joining the points (2, 2) and (4, 0) divides the segment joining the points (1, 2) and (4, 3), then the value of 3 is

Question

If $λ : 1$ is the ratio in which the line joining the points (2, 2) and (4, 0) divides the segment joining the points (1, 2) and (4, 3), then the value of $3 λ$ is ______.

Smart Achievers · Accepted Answer

(1)

$The equation of the line joining the points (2, 2) and (4, 0) is$ $y - 2 = \frac{0 - 2}{4 - 2} (x - 2)$ $\Rightarrow x + y - 4 = 0$ $\dots \dots (i)$

$Suppose the line joining (2, 2) and (4, 0) divides the segment joining (1, 2) and (4, 3)$ $at the point P in the ratio of λ : 1 .$

$Then the coordinates of P are (\frac{4 λ + 1}{λ + 1}, \frac{3 λ + 2}{λ + 1})$

$Clearly, P lies on (i),$

$\Rightarrow$ $\frac{4 λ + 1}{λ + 1} + \frac{3 λ + 2}{λ + 1} - 4 = 0$

$\Rightarrow$ $λ = \frac{1}{3}$

Solution

Q.
If $λ : 1$ is the ratio in which the line joining the points (2, 2) and (4, 0) divides the segment joining the points (1, 2) and (4, 3), then the value of $3 λ$ is ______.

Want Us to Email you About Special Offers & Updates?

Solution

Q. If λ:1 is the ratio in which the line joining the points (2, 2) and (4, 0) divides the segment joining the points (1, 2) and (4, 3), then the value of 3λ is ______.

Want Us to Email you About Special Offers & Updates?

Q.
If $λ : 1$ is the ratio in which the line joining the points (2, 2) and (4, 0) divides the segment joining the points (1, 2) and (4, 3), then the value of $3 λ$ is ______.