1). Find the coordinates of the point that divides the line segment joining \((-2, 3)\) and \((4, 7)\) in the ratio \(3:2\) using the section formula.
2). If a line segment with endpoints \((1, 2)\) and \((5, 6)\) is divided by a point in the ratio \(2:3\), find the coordinates of the dividing point.
3). Given that a line segment joining \((3, -1)\) and \((8, 4)\) is divided by a point in the ratio \(4:5\), calculate the coordinates of the dividing point.
4). Find the point of division for the line segment joining \((2, 1)\) and \((7, 5)\) in the ratio \(1:3\).
5). If a line segment with endpoints \((0, 0)\) and \((6, 12)\) is divided by a point in the ratio \(3:5\), what are the coordinates of the dividing point?
6). Calculate the coordinates of the point that divides the line segment joining \((-3, -4)\) and \((5, 8)\) in the ratio \(2:7\).
7). Given the line segment with endpoints \((-1, 0)\) and \((7, 3)\), determine the coordinates of the point that divides it in the ratio \(2:1\).
8). Find the coordinates of the point which divides the line segment joining \((1, 2)\) and \((9, 8)\) in the ratio \(5:3\).
9). If a line segment with endpoints \((-2, 5)\) and \((6, -1)\) is divided by a point in the ratio \(3:4\), calculate the coordinates of the dividing point.
10). Determine the point of division for the line segment joining \((4, 1)\) and \((10, 5)\) in the ratio \(3:2\).
ANSWERS
1). \((8/5, 27/5)\).
2). \((13/5, 18/5)\).
3). \((47/9, 11/9)\).
4). \((13/4, 2)\).
5). \((18/8, 60/8)\).
6). \((-11/9, -12/9)\).
7). \((13/3, 2)\).
8). \((6, 46/8)\).
9). \((10/7, 17/7)\).
10). \((38/5, 17/5)\).
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