SOLUTION: Can you help me with this assignment in analytic geometry: Find the coordinates of P if it divides the line segment joining A (2,-5) and B ( 6,3) So that r1/r2 = ¾. I need a

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Question 1079370: Can you help me with this assignment in analytic geometry:
Find the coordinates of P if it divides the line segment joining A (2,-5) and B ( 6,3)
So that r1/r2 = ¾.
I need a complete solution. Thank you!

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!



I plotted the points on graph paper and called them A and B and drew AB.  
I drew the vertical line BC and the horizontal line AC, making right 
triangle ABC.

I guessed about where the desired point D would be and drew DE parallel
to AC.

Counting blocks, I noticed that BC = 8 and AC = 4.

By similar triangles DBE and ABC, 

BE + EC = BC = 8

EC = 8 - BE

 



 





}

E is 24/7 units below B, so its y-coordinate is 



That's also the y-coordinate of D.  We need
the x-coordinate of D, so we need to find DE.

By similar triangles DBE and ABC, 







  



Since D is 12/7 units left of E, which has
x-coordinate 6, the x-coordinate of D is



Therefore the answer is



Edwin

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