Question

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6)​

Answer 1

Answer:

Equation of line joining points A(3,−6) and B(5,3)

y−y

1

=

x

2

−x

1

y

2

−y

1

×(x−x

1

)

⟹y+6=

5−2

3+6

(x−3)

⟹3x−y=15

Point of intersection with x−axis is

3x−0=15

⟹x=5

(5,0)

Let the ratio be λ:1

m+n

mx

2

+nx

1

=5⟹

λ+1

3λ+1λ

=5

⟹3λ+5=5λ+5

Also

m+n

my

2

+ny

1

=0

⟹

λ+1

3λ−6×1

=0

⟹λ=2

Ratio is λ:1=2:1