Question

Brochure that has the following problems with solutions.

Find the coordinate of point P that divides the line segment from A(-2,3) and B(1,6) in the ratio
of 1 to 3.

Answer 1

P ≡
`(- (5)/(4), (15)/(4))`

Explanation:

The point P divides the line segment from A(-2,3) and B(1,6) in the ratio of 1 : 3.

So, AP : PB = 1 : 3.

Now, the coordinates of point P will be given by
`((1 * 1 + 3 * (- 2))/(1 + 3), (1 * 6 + 3 * 3)/(1 + 3))`

=
`(- (5)/(4), (15)/(4))` (Answer)

Note: Let there are two points with known coordinates
`(x_(1),y_(1))` and
`(x_(2),y_(2))` and another a point having coordinates (h,k) divides the line joining the two above points internally in the ratio m : n, then (h,k) is given by

(h,k) ≡
`((mx_(2) + nx_(1))/(m + n), (my_(2) + ny_(1))/(m + n))`