Answer:
(0, -[tex]\frac{32}{13}[/tex])
Step-by-step explanation:
If a point (x, y) that divides a line segment having extreme ends [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] into the ratio of m : n,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
From the picture attached,
Extreme ends of a segment are A(-3, -5) and B(10, 6).
Let a point (x, y) divides this segment divides this segment in the ratio of 3 : 10,
x = [tex]\frac{3\times 10+10\times (-3)}{3+10}[/tex]
= 0
y = [tex]\frac{3(6)+10(-5)}{3+10}[/tex]
= [tex]\frac{18-50}{13}[/tex]
= [tex]-\frac{32}{13}[/tex]
Therefore, [tex](0,-\frac{32}{13})[/tex] is a point which divides AB in the ratio of 3 : 10.
