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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

Given The Points X2 5 And Y2 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 41 class=

Sagot :

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.

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

[tex]x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}[/tex]

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

[tex]\begin{gathered} x=\frac{4\times(2)+1\times(-2)}{4+1},y=\frac{4\times(-3)+1\times(5)}{4+1} \\ x=\frac{8-2}{5},y=\frac{-12+5}{5} \\ x=\frac{6}{5},y=\frac{-7}{5} \end{gathered}[/tex]

Therefore, the coordinates of point P are

[tex](\frac{6}{5},-\frac{7}{5})[/tex]

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