Answer:
Point N will be located between 0 and -1.
Step-by-step 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 [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the ratio of m : n is given by,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
By this formula, coordinates of the point N will be,
x = [tex]\frac{3(4)+4(-4)}{3+4}[/tex]
x = [tex]-\frac{4}{7}[/tex]
y = 0
Therefore, coordinates of the point N are [tex](-\frac{4}{7},0)[/tex].
Point N will be located between 0 and -1.
