Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(4, 10), B(14, 15); 3 to 2 The coordinates of P are ( , ).

Answer 1

Since the ratio is 3 to 2, point P will be 3/5 of the distance between point A (4,10) and B(14,15)

first the x-coordinate.

3/5 of the distance between the x-coordinate of A (4) and the x-coordinate of B (14) is 3/5 * (14-4) = 6

the x-coordinate that would be 3/5 of the distance from the x-coordinate of A would be 4 + 6 = 10

second the y coordinate

3/5 of the distance between the y-coordinate of A(10) and the y-coordinate of B (15) is 3/5 * (15-10) = 3

the y-coordinate that would be 3/5 of the distance from the y-coordinate of B would be 10 + 3 = 13

the coordinates of P are thus (10,13)