The coordinates of the point that divides the directed line segment MN with the coordinates of endpoints at M(-4,0) and N(0,4) in the ratio 3:1 are : (-1,3)
Step-by-step explanation:
The coordinates of a point that divides a given line in ration m:n are given by:
[tex](x_p, y_p) = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n})[/tex]
Given
(x1,y1 ) = M(-4,0)
(x2,y2) = N(0,4)
m:n = 3:1
[tex](x_p, y_p) = (\frac{(1)(-4)+(3)(0)}{3+1} , \frac{(1)(0)+(3)(4)}{3+1})\\= (\frac{(-4+0}{4} , \frac{0+12}{4})\\= (\frac{(-4}{4} , \frac{12}{4})\\=(-1,3)[/tex]
Hence,
The coordinates of the point that divides the directed line segment MN with the coordinates of endpoints at M(-4,0) and N(0,4) in the ratio 3:1 are : (-1,3)
Keywords: Coordinate geometry, mid-point
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