You can put this solution on YOUR website!
It would probably help you to see how to solve this problem if you plot the two points P1 at (2,7) and P2 at (8,3) and then draw the line connecting these two points.
Notice that the difference in the x distances between these two points is 6 units. You get that by subtracting the x value of P1 from the x value of P2 and the answer is 8 - 2 = 6.
Then find one-third of that distance ... 6/3 equals 2. Add that to the x value of P1 and you get the x value of the answer. The x value of P1 is 2 and add to that the 2 which you found by taking 1/3 of the x distance between the two points. The answer is an x value of 2 + 2 or 4. So you know the x value of the answer is 4.
From this you can tell that answers A and D cannot be correct because they have an x value that is not 4.
Next you work on the y-difference of the two points. The y value of P2 is 3 and the y value of P1 is 7. Subtract the the two ... 3 - 7 = -4. So one third of this change in y values as you go from P1 to P2 is -4/3. Therefore, starting at the y value of P1 (which is 7) and going -4/3 from that value you get a y value of 7 - 4/3. But 7 is the same as 21/3. So you can use 21/3 - 4/3 and you get the y value of the 1/3 point as being 17/3.
That's the second part of the answer ... and you have the unknown point as being (4, 17/3)
This means that C is the correct answer to this problem.
Hope this helps you to understand the geometry of solving this problem. In summary, since you are looking for the point that is 1/3 of the distance between P1 and P2, you just find 1/3 of the algebraic change in x to get from P1 to P2 and 1/3 of the algebraic change in y to get from P1 to P2 and you add these two values to the x value of P1 and the y value of P1 ... and that gives you the answer.