Question

find the ratio in which point (3,k) divides the segment joining (-6,10) and (4,6)​

Answer 1

Answer:

Answer

Using the section formula, if a point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m

1

:m

2

, then

(x,y)=(

m

1

+m

2

m

1

x

2

+m

2

x

1

,

m

1

+m

2

m

1

y

2

+m

2

y

1

)

Given that ratio m

1

:m

2

=xy

points A(−5,−4) and B(−2,3)

Let ratio be

m

2

m

1

=

1

m

Therefore,

x=

m

1

+m

2

m

1

x

2

+m

2

x

1

−3=

m+1

m.(−2)+(1)(−5)

−3(m+1)=−2m−5

−3m−3=−2m−5

−3+5=−2m+3m

m=2

m

2

m

1

=

1

2

Now, k=

m

1

+m

2

m

1

.y

2

+m

2

.y

1

k=

2+1

2.(3)+1(−4)

k=

3

6−4

k=2/3

∴k=2/3