The coordinates of the point P on directed line segment AB that partitions AB in the ratio 2 to 3 are: [tex](\frac{1}{5},\frac{-12}{5})[/tex]
Step-by-step explanation:
The formula for finding the coordinates of a point that divides the line in ratio m:n are given by:
[tex]P = (\frac{nx_1+mx_2}{m+n},\frac{ny_1+my_2}{m+n} )[/tex]
Here (x1,y1) and (x2,y2) are coordinates of the two points line passed through
Given
(x1,y1) = A(-3,-4)
(x2,y2) = B(5,0)
Ratio: 2:3
m = 2
n = 3
Putting the values in the formula
[tex]P = (\frac{(3)(-3)+(2)(5)}{2+3},\frac{(3)(-4)+(2)(0)}{2+3} )\\P = (\frac{-9+10}{5},\frac{-12+0}{5})\\P = (\frac{1}{5},\frac{-12}{5})[/tex]
Hence,
The coordinates of the point P on directed line segment AB that partitions AB in the ratio 2 to 3 are: [tex](\frac{1}{5},\frac{-12}{5})[/tex]
Keywords: Coordinate geometry, ratio
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