Question

Determine the ratio in which the line 2x+y-4 = 0 divides the line segment joining the
(2-2) and (3,7)
​

Answer 1

Answer:

2 : 9

Step-by-step explanation:

y = - 2x + 4

A(2, - 2) and B(3, 7)

m = ( - 2 - 7) / (2 - 3) = 9

The equation of line passing through point A and B is

y + 2 = 9(x - 2)

y = 9x - 20

$\left \{ {{y=-2x+4} \atop {y=9x - 20}} \right.$

9x + 2x = 24 ⇒ x = 24/11

y = - 48/11 + 4 ⇒ y = - 4/11

P(24/11, - 4/11)

AP = √[(2 - 24/11)² + (- 2 + 4/11)²] = √[(- 2/11)² + (- 18/11)²] = 2√82 / 11

PB = √[(3 -24/11)² + (7 + 4/11)²] = √[(9/11)² + (81/11)²] = 9√82 / 11

AP : PB = (2√82 / 11) : (9√82 / 11)

AP : PB = 2 : 9