Given points A(-2,1) and B(4,5) , find the coordinates of point P along the directed line segment AB so that AP to PB is the ratio 3 to 7.

Answer 1

(-2,1) to (4,5)

are a distance of sqr(16 +36) apart = sqr52 = AB

AP/PB = 3/7 AP = 3/(3+7) = 3/10 = 0.3

AP = 3/10 of AB = .3sqr52 = 2.16

add .3 times the x coordinate difference to -2

.3(6) = 1.8. 1.8-2 = -0.2

add .3 times the y coordinate difference to -2

.3(4) = 1.2, 1.2+1 = 2.2

P is (-0.2, 2.2)

AP = sqr(1.8^2 + 1.2^2) = sqr(=3.24 + 1.44) = sqr(4.65) = 2.16

Answer 2

If AP to PB is the ratio of 3 to 7, then P is 3/10 of the way from A to B.

To find P x coordinate, compute x-coordinate that is 3/10 of the distance from A to B:

3/10 of distance from x coordinate of B to x coordinate of A is 3/10 * (4--2) = 1.8

add that to x coordinate of A = 1.8 + -2 = -0.2

To find P y coordinate, compute y-coordinate that is 3/10 of the distance from A to B:

3/10 of distance from y coordinate of B to x coordinate of A is 3/10 * (5-1) = 1.2

add that to y coordinate of A = 1 + 1.2 = 2.2

P = (-0.2,2.2)