Can someone go step by step over this ratio midpoints question

[fickle wing]

Like i genuinely don't get it so a detailed explanation would be appreciated!!

[radiant hatch]

so to work out midpoint of something you add both numbers then divide by 2 right?

so you form an equation

you know -9+x /2 = 8 so solve that for x coordinate of B

and then do the same for y coordinate

[hazy hinge]

yeah thats one way, a different way would be to see how much the x and y coordinates change by

1. distance from A to midpoint of AB will be the same as AB to B. Because midpoint ratio is 1/2:1/2 (half way on a straight line)
2. Work out the change in coordinates from A to midpoint. change in x is +17, change in y is +5.5
   3, using the idea from point 1, if we add those changes in x and y onto the midpoint we should get B
3. 8 + 17 = 25, so x= 25. 1.5 + 5.5 = 7, so y = 7.
4. therefore B(25,7)

then to check, if you find the midpoint of the line AB, which is done by adding A and B (x,y) coordinates and then dividing by 2

if that equals to the midpoint(8, 1.5) your answer is correct:
difference in x from A to B: 25-9 = 16. 16/2 = 8 CORRECT
difference in y from A to B: 7 -4 = 3. 3/2 = 1.5 CORRECT

[formal snow]

Alright

Basically working x and y