SOLUTION: 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.

Question 1199743: 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.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The description of the problem is actually incomplete; Q could be closer to either A or B. For my response, I will assume it is closer to B.

Determine the x and y coordinates of Q separately. The ratio 4:1 means the differences between both the x and y coordinates will be divided into parts of length 4a and a.

The difference in the x coordinates of A and B is +2:
4a+a = 2
5a = 2
a = 2/5

The x coordinate of Q is 2+4a = 2+4(2/5) = 2+8/5 = 18/5 or 3.6.

The difference in the y coordinates of A and B is +3:
4a+a = 3
5a = 3
a = 3/5

The y coordinate of Q is -1+4a = -1+12/5 = 7/5 or 1.4

ANSWER: Q(3.6,1.4)

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