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. Show all your work for full credit.

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): You can put this solution on YOUR website!
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.
.
Let A ~(x1,y1)
C~(x2,y2)
and
Q~ (x,y)
Formula

(4*4+1*2)/(4+1)= 3.6

((4*2+1*(-1))/5 = 7/5 =1.4
Q (3.6,1.4)

Answer by greenestamps(13215)   (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): You can put this solution on YOUR website!

Answer: Q(3.6, 1.4)

Reason:

Refer to this image

We split segment AB into 5 pieces (because we add the parts of the ratio 4:1)
AB = 2 units long
AB/5 = 2/5 = 0.4
Each space is 0.4 units (eg: EF = 0.4)

Start at A and move 4 spaces to the right to arrive at G(3.6,-1)
Go straight up along the dashed line to arrive at point Q(3.6, 1.4)

A similar process is carried out for the vertical segment BC.
BC = 3 units
BC/5 = 3/5 = 0.6
Each smaller piece is 0.6 units long
eg: segment JK = 0.6
We start at B and move 4 spaces up to arrive at K, which is the same height as point Q (as noted by the dashed line).

Another approach would be to use the formula mentioned in this lesson
https://www.algebra.com/algebra/homework/formulas/split-segment-n-pieces.lesson
and here is an example problem that uses that formula
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1197813.html
Although you won't have to worry about every red point in that example.

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