Question

if the line 2x + Y equal ke passes through the point which divides the line segment joining the points (1, 1) and (2,4) in the ratio 3:2 then K equals?
1) 11/5
2) 29/5
3) 5
4) 6 ​

Answer 1

ANSWER:

• The value of K = 6

GIVEN:

• The line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2,4) in the ratio 3:2.

TO FIND:

• The value of k.

EXPLANATION:

$\boxed{ \bold{ \gray{Internally = \dfrac{mx_2 +nx_1}{m+n},\ \dfrac{my_2 +ny_1}{m+n}}}}$

m = 3, n = 2

$\sf(x_1,\ x_2) = (1,\ 2)$

$\sf(y_1,\ y_2) = (1,\ 4)$

$\sf Internally = \dfrac{3(2) +2(1)}{3 + 2},\ \dfrac{3(4) +2(1)}{3 + 2}$

$\sf Internally = \dfrac{6 + 2}{5},\ \dfrac{12 + 2}{5}$

$\sf Internally = \dfrac{8}{5},\ \dfrac{14}{5}$

The line 2x + y = k passes through the point which divides the line segment joining the points.

$\sf (x , \ y) = \left( \dfrac{8}{5},\ \dfrac{14}{5} \right)$

$\sf 2\left( \dfrac{8}{5} \right) + \left( \dfrac{14}{5} \right) = k$

$\sf \left( \dfrac{16}{5} \right) + \left( \dfrac{14}{5} \right) = k$

$\sf \left( \dfrac{16 + 14}{5} \right) = k$

$\sf k = 6$

HENCE THE VALUE OF K = 6.