Question

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

Answer 1

(0, -
`(32)/(13)`)

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

and y =
`(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 =
`(3* 10+10* (-3))/(3+10)`

= 0

y =
`(3(6)+10(-5))/(3+10)`

=
`(18-50)/(13)`

=
`-(32)/(13)`

Therefore,
`(0,-(32)/(13))` is a point which divides AB in the ratio of 3 : 10.