Question

Find a number t such that the distance between (-2,1) and (3t, 2t) is as small as possible.

Answer 1

What's the distance formula?

Answer 2

d = sqrt( (x2-x1)^2 + (y2-y1)^2 )

Answer 3

d = sqrt( (3t+2)^2 + (2t-1)^2 )

Answer 4

d = sqrt( (9t^2+12t+4) + (4t^2-4t+1) )
d = sqrt( 9t^2 + 4t^2 + 12t - 4t + 4 + 1 )

Answer 5

d = sqrt (13t^2 + 8t + 5)
d' = (1/2) (13t^2 + 8t + 5)^(-1/2)*(26t+8)

Answer 6

So now solve:
26t+8 = 0
and
13t^2 + 8t + 5 = 0
Get your ts and plug them all into d = sqrt( (3t+2)^2 + (2t-1)^2 ).
See at which t d is smallest, and that will be your t.