Step 1: Identify the coordinates of points r and s
The points r and s are given to us. Point r has coordinates (1, 2) and point s has coordinates (4, 6).
Step 2: Find the vector from r to s.
The vector from r to s (let's call this rs) can be found by subtracting the coordinates of r from the coordinates of s.
This gives us rs = (4 - 1, 6 - 2) = (3, 4).
Step 3: Find the vector from r to q (rq)
Since we know that q is 25% of the distance from r to s or 0.25 times the vector rs, we can find vector rq by multiplying vector rs by 0.25.
This gives us rq = 0.25 * rs = 0.25 * (3, 4) = (0.75, 1).
Step 4: Find the coordinates of q
To find the coordinates of q, we simply add vector rq to the coordinates of r.
This gives us q = r + rq = (1, 2) + (0.75, 1) = (1.75, 3).
So, the coordinates of point q are (1.75, 3).
Therefore, by finding the vectors between the points and performing simple operations on them, we were able to find the coordinates of the point that is 25% of the distance from r to s.