A point Q on a segment points 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.

Step-by-step explanation:

We are given a ratio for this problem so we will use the formula for when we are given a ratio (as opposed to the formula for when you are given that the point you're looking for is a fraction of the way from one point to another, like 1/3 of the way from point A to point B. That's a different formula).

The formulas are for the x and y coordinates of the point in question:

  and   where

a = 4 (from the ratio),

b = 1 (from the ratio),

x1= 2, y1 = -1 (from point A) and

x2 = 4, y2 = 2 (from point C). The coordinates of Q are found by filling in. Let's do x first:

which gives us

and then y:

which gives us

Therefore, the coordinates of Q are

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step-by-step explanation: