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An ant started moving from the point A($2, 3$) and moved along the line segment AB. It covered three-fourth of the distance AB and reached at a point C($x, y$). If the coordinates of the point B are ($10, 15$), find the coordinates of the point C.
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Solution
Point C divides AB in the ratio $3: 1$ (1/2 Mark)
$x = \frac{3(10) + 1(2)}{3+1} = 8$ (1/2 Mark)
$y = \frac{3(15) + 1(3)}{3+1} = 12$ (1/2 Mark)
coordinates of the point C are ($8,12$) (1/2 Mark)
Point C divides AB in the ratio $3: 1$ (1/2 Mark)
$x = \frac{3(10) + 1(2)}{3+1} = 8$ (1/2 Mark)
$y = \frac{3(15) + 1(3)}{3+1} = 12$ (1/2 Mark)
coordinates of the point C are ($8,12$) (1/2 Mark)