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?

Guest May 10, 2019

edited by
Guest
May 10, 2019

edited by Guest May 10, 2019

edited by Guest May 10, 2019

#1**+2 **

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

CPhill May 10, 2019