Question 1201988: 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. Show all your work for full credit.
Found 3 solutions by mananth, greenestamps, math_tutor2020:
Answer by mananth(16946)   (Show Source):
Answer by greenestamps(13214)  (Show Source):
You can put this solution on YOUR website!
It is likely that, in the resource you are using, there is a formula like the one shown by the other tutor for solving this problem.
If you like using formulas to solve problems, then go ahead and do it that way.
But mathematics will be more enjoyable if you understand what you are doing to solve the problem, instead of plugging numbers into formulas.
In this problem, the point Q divides line segment AC in the ratio 4:1. That means Q is 4/5 of the way from A to C.
So the x coordinate of Q will be 4/5 of the way from the x coordinate of A to the x coordinate of C; and similarly for the y coordinate of Q.
The difference between the x coordinates of A and C is 4-2 = 2; 4/5 of 2 is 1.6; the x coordinate of Q is 1.6 more than the x coordinate of A: 2+1.6 = 3.6.
The difference between the y coordinates of A and C is 2-(-1) = 3; 4/5 of 3 is 2.4; the y coordinate of Q is 2.4 more than the y coordinate of A: -1+2.4 = 1.4.
ANSWER: Q(3.6,1.4)
Answer by math_tutor2020(3817)  (Show Source):
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