A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio. Find Q. You must show all work to receive credit. please don't put a fake answer! I really need to pass this test. thank you :))

I believe:

Answer
Q = (3.5, 1.25)
Step-by-step explanation:
Point Q must satisfy the requirement ...
QA : QC = 3 : 1 . . . . . . the desired ratio of segment lengths
(Q -A)/(C -Q) = 3/1 . . . . keeping the points in the same order
Q -A = 3(C -Q) . . . . . . multiply by (C-Q)
4Q = 3C +A . . . . . . . . add 3Q
Q = (3C +A)/4 . . . . . . the equation for finding Q*
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Q = (3(4, 2) +(2, -1))/4 = (12+2, 6-1)/4 = (14/4, 5/4)
Q = (3.5, 1.25)

* You will note that this is a weighted average of the end points, where the weights are the reverse of the relative segment lengths. That is the end point connected to the shorter segment has the weight associated with the length of the longer segment. This same rule applies to any problem involving partitioning of segments. It also applies to any mixture problem.