If A and B are (-2,-2) and (2,-4). Find the coordinates P such that AP=3/7 AB and P lies on the line segment ab

Question

asked Oct 9, 2022 130k views

1 Answer

Cluny · Answer 1 · 2022-10-15T05:09:11+0000

Answer:

The coordinates of point P are
(-(2)/(7), -(20)/(7)) .

Explanation:

Point P:

The coordinates of point P are (x,y).

AP=3/7 AB

So

P - A = (3)/(7)(B-A)

We apply this both for coordinate x and coordinate y.

Coordinate x:

x - (-2) = (3)/(7)(2 - (-2))

x + 2 = (12)/(7)

x = (12)/(7) - 2 = (12)/(7) - (14)/(7) = -(2)/(7)

Coordinate y:

y - (-2) = (3)/(7)(-4 - (-2))

y + 2 = -(6)/(7)

y = -(6)/(7) - 2 = -(6)/(7) - (14)/(7) = -(20)/(7)

The coordinates of point P are
(-(2)/(7), -(20)/(7)) .