A point Q on a segment with endpoints A(2, −1) and C(4, 2) partitions the segment in a 3:1 ratio. Find Q. You must show all work to receive credit. (10 points)

The length of the segment is:

D= sqrt((4-2)^2 + (2- -1)^2 =

Sqrt( 2^2 + 3^2) =

Sqrt( 4 + 9) = sqrt(13) = 3.6055

The ratio is 3:1 so q is 3/4 of the way to point c

Q = 3/4 x sqrt(13)

Q = 3sqrt(13)/4 exact answer

Q = 2.7041 as a decimal answer

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula