Now remember with this situation, 5:3 is not 5/3, but rather it's "5 equal parts to 3 equal parts", which is a total of 8 equal parts. This problem wants you to place point M at 5/8 the distance from A to B.
Firstly, how many units apart is -4 to 4 (the x-coordinates)? That's 8 units. Multiply 5/8 by 8:
[tex]\frac{5}{8}\times\frac{8}{1}=\frac{40}{8}=5[/tex]
Next, how many units apart is -2 to -10 (the y-coordinates)? That's 8 units as well. Multiply 5/8 by 8.
[tex]\frac{5}{8}\times\frac{8}{1}=\frac{40}{8}=5[/tex]
Now, since from -4 to 4 you are increasing, add 5 to -4:
[tex]-4+5=1[/tex]
1 is your x-coordinate.
Now since from -2 to -10 you are decreasing, subtract 5 from -2:
[tex]-2-5=-7[/tex]
-7 is your y-coordinate.
Putting it all together, point M is at (1,-7), or A.
