Question

Find the ratio in which the line segment joining (-3,-4) and (3,5) is divided by (x,2). Also, find x.

Answer 1

Answer:

The line segment is (3,−3) and B(−2,7)

Let the point on x - axis be (x,0) which divides the line in the ratio of m:n. Then,

using section formula,

(x,y)=(

m+n

m×x

2

+n×x

1

,

m+n

m×y

2

+n×y

1

)

0=

m+n

7m−3n

7m=3n

n

m

=

7

3

Thus, the coordinates of x-axis will be:

x=

7+3

3(−2)+7(3)

x=

10

15

=

2

3

Thus, the line segment AB is divided in the ratio

7

3

at the point (

2

3

,0)

Thus, 2 times the x-coordinate is 3