Question

Point N is 3/4 of the distance from A to D. Where is point N?

Answer 1

Point N will be located between 0 and -1.

Explanation:

Points A and D are placed at (-4, 0) and (4, 0) on a number line.

We have to find the location of a point N which divides AD in the ratio of 3 : 4.

Coordinates of a point (x, y) which divides a segment with extreme ends at
`(x_1,y_1)` and
`(x_2,y_2)` in the ratio of m : n is given by,

x =
`(mx_2+nx_1)/(m+n)`

y =
`(my_2+ny_1)/(m+n)`

By this formula, coordinates of the point N will be,

x =
`(3(4)+4(-4))/(3+4)`

x =
`-(4)/(7)`

y = 0

Therefore, coordinates of the point N are
`(-(4)/(7),0)`.

Point N will be located between 0 and -1.