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Q.

The ratio in which the point P(3,5) divides the line segment AB where A(1,3) and B(7,9) is ____.


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Detailed Solution

Let the point P(3,5) divide the line segment joining the points A(1,3) and B(7,9) in the ratio k:1
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" width="176" height="36" alt=The points (x,y) here are (3,5).
{"mathml":"<math class="image_resized" style="width:96px;height:142px"><span style="font-family:Since, the ratio is k:1, the ratio is 1.2
 
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The ratio in which the point P(3,5) divides the line segment AB where A(1,3) and B(7,9) is ____.