Question

Find the coordinates of point P along the directed like segment AB from A(1,6) to B(-2,-3) so that the ratio of AP to PB is 5 to 1

Answer 1

The coordinates of
`P = (x,y) = (-(3)/(2) , -(3)/(2))`

Explanation:

Coordinates of A= (1,6) and B = (-2,-3)

AP:PB = 5:1

Let the coordinates of P =(x,y)

Now, by SECTION FORMULA:

If m1: m2 is the ratio between two segments, then the coordinate of point is given as
`(x,y) = ((m1x_2+ m2x_1)/(m1+m2) ,  (m1y_2+ m2y_1)/(m1+m2) )`

Similarly here, (x1, y1) = (1,6) , (x2, y2) = (-2,-3) and m1: m2 = 5: 1

Putting all values in equation, we get:

`(x,y) = ((5(-2)+ 1(1))/(5+1) ,  (5(-3)+1(6))/(5+1) )`

or,
`(x,y) = ((-10 + 1)/(6) , (-15 + 6)/(6) )  = ((-9)/(6) , (-9)/(6) )`

Hence, the coordinates of
`P = (x,y) = (-(3)/(2) , -(3)/(2))`