Question

Given the points A(-3, 1) and B(4,8), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio 5:2.

Answer 1

If P(xp,yp) divides a line segment from A(x1,y1) to B(x2,y2) in the ratio a:b, then:

xp = x1 + (a/(a+b))* (x2 - x1)

yp = y1 + (a/(a+b))* (y2 - y1)

In this case:

a = 5

b = 2

x1 = -3

y1 = 1

x2 = 4

y2 = 8

Replacing the data into the equations:

xp = -3 + (5/7) * (4- (-3)) = -3 + (5/7)*(7) = -3 + 5 = 2

yp = 1 + (5/7) *( 8 - 1) = 1 + (5/7)*(7) = 1 + 5 = 6

Therefore, the coordinates of the point P are:

(xp,yp) = (2,6)