Question

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

Answer 1

The given endpoints are A (-1, 2) and B (7, 8).

Let the coordinates of P be (x,y)
Because AP:PB = 1:3, therefore
$\frac{x-(-1)}{7-x} = \frac{1}{3}$
Cross multiply.
3(x+1) = 7 - x
3x + 3 = 7 - x
4x = 4
x = 1

Also,
$\frac{y-2}{8-y} = \frac{1}{3}$
Cross multiply.
3(y - 2) = 8 - y
3y - 6 = 8 - y
4y = 14
y = 7/2

Answer:
The coordinates of P are (1, 7/2)