NDA 2023 Maths · Mathematics · Straight Lines · hard

The line joining (2,-3) and (6,5) is cut by the y-axis in the ratio

Single correct option

The line joining

(2,-3)

and

(6,5)

is cut by the

y

-axis in the ratio

Show answer and solution

Answer: (B) externally $1:3$

Let the

y

-axis divide the segment in the ratio

k:1

. Then the

x

-coordinate is

\dfrac{6k+2}{k+1}=0

, giving

k=-\dfrac13

. A negative ratio means external division, in the ratio

1:3

. Both end points lie on the same side of the

y

-axis (

x=2

and

x=6

), which also shows that the division cannot be internal.

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