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Let A,B be the points on the coordinate plane with coordinates (t-4 , -1) and (-2 , t-3) respectively. The square of the distance between the midpoint of line AB and an endpoint of line AB is equal to (t^2)/2. What is the value of t?

 May 10, 2019
edited by Guest  May 10, 2019
edited by Guest  May 10, 2019
 #1
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Let A,B be the points on the coordinate plane with coordinates (t-4 , -1) and (-2 , t-3) respectively. The square of the distance between the midpoint of line AB and an endpoint of line AB is equal to (t^2)/2. What is the value of t?

 

 

Midpoint  of AB  =  [  (t - 4 - 2) / 2  , (t - 3 - 1) / 2 ]   =  [ (t - 6)/2, (t - 4)/2 ]

 

Square of distance between  A  and midpoint  =

 

[ (t - 6)/2 - (t - 4) ]^2 + [ (t - 4)/2+ 1}^2  =

 

[ (t/2 - 3 - t + 4 ] ^2  +  [ t/2 -2 + 1 ]^2  =

 

[ 1 - (1/2)t ]^2  + [ t/2 - 1]^2  =

 

(1/4)t^2 - t + 1  + (1/4)t^2 - t + 1        [set this equal to  (1/2)t^2 ]

 

(1/2)t^2  - 2t + 2  =   (1/2)t^2

 

 

-2t + 2  = 0

 

t = 1

 

 

 

cool cool cool

 May 10, 2019

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