Question

1) Point M divides line segment AB, in the direction from A to B. in a ratio of 4 to 9. What value on the number line

would indicate the location of point M?​

Answer 1

Point M will be located between 0 and 1 at
`(1)/(13)`.

Explanation:

Two points A and B have been given on a number line.

Point A is at -3 and point B at 7.

Distance between these points AB = 7 - (-3)

= 7 + 3

= 10 units

Another point M divides the given segment AB in the ratio of 4 : 9.

Therefore, length of segment AM will be =
`(4* 10)/((4+9))`

=
`(40)/(13)`

=
`3(1)/(13)` units

Now the position of point M will be at
`(-3+3(1)/(13))` =
`(1)/(13)`

Therefore, point M will be located between 0 and 1 at
`(1)/(13)`.