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Q.

Find the ratio in which the points (2,6) divides the line segment joining the points (-2,2) and (3,7).


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a

1:2

b

4:1

c

3:1

d

1:1 

answer is B.

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Detailed Solution

Let the point (2,6) divide the line segment joining the points (-2,2) and (3,7) in the ratio k:1
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" width="176" height="36" alt=The points (x,y) here are (2,6).
{"mathml":"<math class="image_resized" style="width:96px;height:90px"><span style="font-family:Since the ratio is k:1, the ratio is 4:1.
 
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