Question

Given the points X(-2, 5) and Y(2, -3), find the coordinates of the point P on directed line segment XY that partitions segment XY such that the ratio of XP to PY is 4:1

Answer 1

Given:

given points are X(-2,5) and Y(2,-3).

Find:

we have to find the coordinates of the point P on directed line segment XY that partitions the segment XY in such a way that the ratio of XP:PY = 4:1.

Step-by-step explanation:

we will use section formula to find the coordinates of point P,

If a line XY is divided into two sections in the ratio m:n, then the x and y coordinates of point P are

`x=(mx_2+nx_1)/(m+n),y=(my_2+ny_1)/(m+n)`

here, m = 4 and n = 1 and the points x1= -2, x2 = 2, y1 = 5 and y2= -3.

Therefore, the coordinates of point P are

`\begin{gathered} x=(4*(2)+1*(-2))/(4+1),y=(4*(-3)+1*(5))/(4+1) \\ x=(8-2)/(5),y=(-12+5)/(5) \\ x=(6)/(5),y=(-7)/(5) \end{gathered}`

Therefore, the coordinates of point P are

`((6)/(5),-(7)/(5))`