Question

find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-4,-8), B(0,0) ; 3 to 1

Answer 1

Answer:

The coordinate of point P along the directed line segment AB is ( - 1 , - 2 )

Step-by-step explanation:

Given as :

The coordinate of the points A = ( - 4 , - 8 )

The coordinate of the points B = ( 0 , 0 )

The Point P divide the line joining points A and B in the ratio m : n = 3 : 1

Let The coordinates of the points P = ( x , y )

So, x = $\dfrac{mx_2 + nx_1}{m + n}$

And y = $\dfrac{my_2 + ny_1}{m + n}$

∴  x =  $\dfrac{mx_2 + nx_1}{m + n}$

Or, x = $\frac{3\times 0+1\times (-4)}{3 + 1}$

Or, x = $\frac{0-4}{4}$

∴   x = - 1

Similarly

    y =  $\dfrac{my_2 + ny_1}{m + n}$

Or, y = $\frac{3\times 0+1\times (-8)}{3 + 1}$

Or, y = $\frac{0-8}{4}$

∴   y = - 2

so, coordinate of P ( x , y ) = ( - 1 , - 2 )

Hence The coordinate of point P along the directed line segment AB is     ( - 1 , - 2 )  Answer