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

Algebra ->  Triangles -> 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      Log On


   

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) About Me  (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, %22BD%22%2F%22DA%22=%22BE%22%2F%22EC%22=3%2F4

BE + EC = BC = 8

EC = 8 - BE

%22BE%22%2F%22EC%22=3%2F4 

4%2A%22BE%22=3%2A%22EC%22

4%2A%22BE%22=3%2A%288-%22BE%22%29 

4%2A%22BE%22=24-3%2A%22BE%22

7%2A%22BE%22=24

%22BE%22=24%2F7}

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

3-24%2F7=21%2F7-24%2F7=-3%2F7

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, 

%22DE%22%2F%22AC%22=%22BE%22%2F%22BC%22

%22DE%22%2A%22BC%22=%22BE%22%2A%22AC%22

%22DE%22%2A8=expr%2824%2F7%29%2A4

%22DE%22%2A8=96%2F7  

%22DE%22=12%2F7

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

6-12%2F7=42%2F7-12%2F7=30%2F7

Therefore the answer is



Edwin