Question

The endpoints of the directed line segment AB are A(-1 2) and B (7 8). Find the coordinates of point P along AB so that the ratio of AP to PB is 1 to 3

Answer 1

The coordinates of P are (1,3.5)

Explanation:

Here, we simply want to find the coordinates of point P that divides line AB in the ratio 1 to 3

Mathematically, that would be;

(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)

where in this case m = 1, n = 3

(x1,y1) = (-1,2)

(x2,y2) = (7,8)

Thus, we have ;

(x,y) = (3(-1) + 1(7)/)1+3) , (3)2) + 1(8)/(1 + 3)

(x,y) = (-3+7)/4 , (6 + 8)/4

(x,y) = 4/4, 14/4

(x,y) = (1,3.5)