So despite what you may think, 1:4 is not 1/4 in this situation, but rather it's "1 equal part to 4 equal parts", which is a total of 5 equal parts. In short, they are asking you for the point at the 1/5 mark from A to B.
Firstly, how many units apart is 10 to 2 (the x-coordinates)? That would be 8 units. Multiply 1/5 by 8:
[tex]\frac{1}{5}\times \frac{8}{1}=\frac{8}{5}[/tex]
Next, how many units apart is 4 to 8 (the y-coordinates)? That would be 4 units. Multiply 1/5 by 4:
[tex]\frac{1}{5}\times \frac{4}{1}=\frac{4}{5}[/tex]
Now, since from 10 to 2 you are decreasing, subtract 8/5 from 10:
[tex]\frac{10}{1}\times \frac{5}{5}=\frac{50}{5}\\\\\frac{50}{5}-\frac{8}{5}=\frac{42}{5}[/tex]
42/5 is the x-coordinate.
Now, since from 4 to 8 you are increasing, add 4/5 to 4:
[tex]4+\frac{4}{5}=4\frac{4}{5}=\frac{24}{5}[/tex]
24/5 is the y-coordinate.
Putting it together, the point is (42/5, 24/5), or D.
