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Endpoint: (5/3, 1 2/11) Midpoint: (1 7/12, 4 2/3) find the second Endpoint

 Sep 10, 2014

Best Answer 

 #1
avatar+129840 
+5

Let's call the second endpoint (x1 , y1)....and by the midpoint formula, we have

(x1 + 5/3)/2  = 1 + 7/12   and (y1 + 1 + 2/11)/2 = 4 + 2/3 

And converting 1 + 7/12 to  19/12 and  solving the first equation, we have

(x1 + 5/3)/2  = 19/12      multiply both sides by 2

x1 + 5/3  = 38/12      subtract 5/3 from both sides

x1 = 38/12 - 5/3 = 3/2

And converting 1 + 2/11 to 13/11 and 4 + 2/3 to 14/3  and proceeding as before, we have

(y1 + 13/11)/2  = 14/3    multiply both sides by 2

(y1 + 13/11)  = 28/3      subtract 13/11 from each side

(y1  = 28/3 - 13/11 = 269/33

So, the other endpoint is (3/2, 269/33)

 

 Sep 10, 2014
 #1
avatar+129840 
+5
Best Answer

Let's call the second endpoint (x1 , y1)....and by the midpoint formula, we have

(x1 + 5/3)/2  = 1 + 7/12   and (y1 + 1 + 2/11)/2 = 4 + 2/3 

And converting 1 + 7/12 to  19/12 and  solving the first equation, we have

(x1 + 5/3)/2  = 19/12      multiply both sides by 2

x1 + 5/3  = 38/12      subtract 5/3 from both sides

x1 = 38/12 - 5/3 = 3/2

And converting 1 + 2/11 to 13/11 and 4 + 2/3 to 14/3  and proceeding as before, we have

(y1 + 13/11)/2  = 14/3    multiply both sides by 2

(y1 + 13/11)  = 28/3      subtract 13/11 from each side

(y1  = 28/3 - 13/11 = 269/33

So, the other endpoint is (3/2, 269/33)

 

CPhill Sep 10, 2014

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