Respuesta :

When a line segment with point A with the co-ordinates (x1, y1) and point B with the co-ordinates (x2,y2) is divided into the ratio m:n by a point P, we find the x-coordinate of the point by using the following formula: (mx2+nx1)/m+n and the y-coordinate by using this formula: (ny1+my2)/n+m
x-coordinate of P=[(1x7)+(2x-2)]/1+2=1
y-coordinate of Q=[(2x4)+(1x-2)]/2+1=2
Ans: P=(1,2)
abidemiokin

The coordinates of the point P on directed line segment that partitions AB in the ratio 1:2 is (4, 0)

Given the point A (-2, 4) and B(7, -2). The coordinate of the point P on the line segment that partitions AB in the ratio 1:2, is expressed as:

[tex]P(X, Y) = (\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})[/tex]

Substitute the given coordinates where a = 1 and b = 2

[tex]P(X, Y) = (\frac{1(-2)+2(7)}{1+3}, \frac{1(4)+2(-2)}{1+2})\\P(X, Y) = (\frac{-2+14}{3}, \frac{4-4}{1+2})\\P(X, Y) = (\frac{12}{3},\frac{0}{3})\\P(X, Y) = (4, 0)\\[/tex]

Hence the coordinate of point P is (4, 0)

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