Question

The ratio in which the line 2x + y - 6 = 0
divides the line segment joining the points
P(1, 1) and Q(7, 7) isq

Answer 1

Answer:

$The ratio in which the line 2x + y - 6 = 0</p><p>divides the line segment joining the points</p><p>P(1, 1) and Q(7, 7) isq$

Answer 2

2x + y -6 = 0

x + y = 2 ( p(x,y) = P (1,1)______(1)

2x + y = 6 »»»» y = 6 - 2x _____(2)

By elimination method

eqn (2) - eqn (1)

2x + y = 6

x + y = 2 (Symbols will be changed)

x = 4

Substitute x = 4 in (1)

x + y = 1

4 + y = 1

y = 1 - 3

y = -2

So,

The points which divides the line segment are (x,y) = (4,-2)

Given

• P(1, 1) = P(x1, y1)
• Q(7, 7) = Q (x2, y2)
• Ratio = m1:m2 = ?

We know

P(x,y) = {m1x2+m2x1} , {m1y2 + m2y1}

{ m1 + m2 } { m1 + m2 }

Taking only P (x)

P(x) = {m1x2+m2x1}

{ m1 + m2 }

P(1) = m1(7) + m2(1)

m1 + m2

P (1) = 7m1 +2m2

m1 + m2

1 = 7m1 + 2m2

m1 + m2

m1 + m2 = 7m1 + 2m2

m1 - 7m1 = 2m2 - m2

-6m1 = 1m2

m1 = 1

m2 -6

m1 : m2 = 1 : -6

Therefore,

The ratio in which the line 2x + y - 6 = 0

divides the line segment joining the points

P(1, 1) and Q(7, 7) is 1 : -6