Given points M( 3, 4) and N( -2, -6), find the coordinates of the point on directed line segment MN that partitions MN in the ratio 3:2
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Let coordinates of point M(3, 4) be x1 and y1 respectively and those of point N(-2, -6) be x2 and y2 respectively.
Ratio=m:n=3:2
x coordinate of the point= (m*x2+n*x1)/(m+n)
y coordinate of the point=(m*y2+n*y1)/(m+n)
Note- the values of x1,x2,y1,y2 have to be taken with their signs.
Using the formula-
x=(3*-2)+(2*3)/3+2
=(-6+6)/5=0/5=0
y=(3*-6)+(2*4)/(3+2)
=(-18+8)/5=-10/5=-2
Hence, coordinates of required point are (0, -2)
Ratio=m:n=3:2
x coordinate of the point= (m*x2+n*x1)/(m+n)
y coordinate of the point=(m*y2+n*y1)/(m+n)
Note- the values of x1,x2,y1,y2 have to be taken with their signs.
Using the formula-
x=(3*-2)+(2*3)/3+2
=(-6+6)/5=0/5=0
y=(3*-6)+(2*4)/(3+2)
=(-18+8)/5=-10/5=-2
Hence, coordinates of required point are (0, -2)
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