Question

Point C is located at (1, 2) and point D is located at (−4, −2). Find the x value for the point that is 1\4 the distance from point C to point D

Answer 1

The easiest way to do this is to realize this is a weighted average of the two points.  (A weighted average is a linear combination where the coefficients add to one.)

(x,y) = (1-t)C + tD

where t is a real parameter. When t=0 we're at point C, when t=1 we're at point D. We're interested in t=1/4,

(x,y)= (3/4) C + (1/4) D

We're only asked for the x coordinate:

x = (3/4) (1) + (1/4) (-4) = 3/4 - 1 = - 1/4

Answer: $\quad - \dfrac 1 4$