Question

15. Find the ratio in which the y-axis divides the line segment joining the points (7,3) and (-4,5). Also find the coordinates of t he point of intersection.

2​

Answer 1

Step-by-step explanation:

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Find the ratio in which the y-axis divides the line segment joining the points (5,−6) and (−1,−4). Also, find the coordinates of the point of division.

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Solution

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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:n, then

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let the required ratio be m:n

here,x

1

=5,x

2

=−1,y

1

=−6,y

2

=−4

Then, According to question, we have ;

m+n

mx

2

+mx

1

=0

⇒m(−1)+n(5)=0

⇒5n=m

⇒m=5n

⇒

n

m

=

1

5

⇒m:n=5:1

Coordinate of the point of division

=(0,

m+n

my

2

+my

1

)

=(0,

6

5(−4)+1(−6)

)

=(0,

6

−20−6

)

=(0,

3

−13

)