Answer:
Option (3)
Step-by-step explanation:
Coordinates of a point (h, k) which divides a line with ends [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the ratio of m : n are,
h = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
k = [tex]\frac{my_2+ny_1}{m+n}[/tex]
If the ends of line AB are A(-5, -4) and B(5, 1) and a point (h, k) divides this line into two parts in the ratio of 3 : 2
h = [tex]\frac{3\times (5)+2(-5)}{3+2}[/tex]
h = 1
k = [tex]\frac{3(1)+2(-4)}{3+2}[/tex]
k = -1
Therefore, coordinates of the point (h, k) are (1, -1).
Option (3) will be the answer.
