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

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

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

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