Answer:
The answer is point (4,8)
Explanation:
The horizontal (x) distance between the given points is 6-1 = 5.
If the horizontal distance is 5, then because the ratio of the given points is 3 to 2, we can say that 3/5 of 5 is 3. The horizontal distance between (1,5) and (x,y) is 3, so x = 4.
We can do the same with the vertical (y) distance, which is 10-5 = 5.
Again, 3/5 of 5 is 3, so y = 5+3 = 8
Answer: the point is (4,8).
CHECK: We can check this result by finding the distances between the given points to (4,8), and calculating the distance.
Distance between (1,5) and (4,8) = √18 = 3√2
Distance between (6,10) and (4,8) = √8 = 2√2
The ratio between the distances is 3:2, so the solution checks out.