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?
+128473 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
