Question

The coordinates of the point 3/10 of the way from A to B are

Answer 1

Answer:

(0, -$\frac{32}{13}$)

Step-by-step explanation:

If a point (x, y) that divides a line segment having extreme ends $(x_1,y_1)$ and $(x_2,y_2)$ into the ratio of m : n,

x = $\frac{mx_2+nx_1}{m+n}$

and y = $\frac{my_2+ny_1}{m+n}$

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 = $\frac{3\times 10+10\times (-3)}{3+10}$

  = 0

y = $\frac{3(6)+10(-5)}{3+10}$

  = $\frac{18-50}{13}$

  = $-\frac{32}{13}$

Therefore, $(0,-\frac{32}{13})$ is a point which divides AB in the ratio of 3 : 10.