in what ratio does the point (24/11 ,y)divide the line segment joining the points P(2,-2) and Q(3,7)?also find the value of y.
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Let , A=(2,-2).
and B=(3,7)
point on the line AB=C=(24/11,y)
Section formula:
{ (m1x2+m2x1)/(m1+m2),(m1y2+m2y1)/(m1+m2)}
C(24/11,y)={(3m1+2m2)/(m1+m2),(7m1-2m2)/(m1+m2)}
On comparing co-ordinates we get,
24/11=(3m1+2m2)/(m1+m2)
24m1+24m2=33m1+22m2
2m2=9m1
m1/m2=2/9
Therefore ratio=2:9
Now substituting above ratio in y-coordinate we get,
y=(7m1-2m2)/(m1+m2)
y=(2×7-9×2)/(2+9)
y=(14-18)/11
y=-4/11
Hence the required ratio =2:9
and the value of y=-4/11
and B=(3,7)
point on the line AB=C=(24/11,y)
Section formula:
{ (m1x2+m2x1)/(m1+m2),(m1y2+m2y1)/(m1+m2)}
C(24/11,y)={(3m1+2m2)/(m1+m2),(7m1-2m2)/(m1+m2)}
On comparing co-ordinates we get,
24/11=(3m1+2m2)/(m1+m2)
24m1+24m2=33m1+22m2
2m2=9m1
m1/m2=2/9
Therefore ratio=2:9
Now substituting above ratio in y-coordinate we get,
y=(7m1-2m2)/(m1+m2)
y=(2×7-9×2)/(2+9)
y=(14-18)/11
y=-4/11
Hence the required ratio =2:9
and the value of y=-4/11
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