A ratio of 1:2 means that HI is one-third of the length of HJ. Why? There are three equal parts. HI is one part, and IJ is the second part, but it is twice as long as HI.
So HI is 1/3 of the total distance from H to J, and IJ is 2/3 of the whole distance.
All we have to do is find the x-distance between the points, divide that by three, and add it to the x-value of H.
Then, we repeat that for the y-distance, adding the value found to the y-value of H.
The x-distance between H and J is
x2 - x1 = 8 - (-4) = 8 + 4 = 12
(1/3) of 12 is 4
x1 + (1/3)×12 = (-4) + 4 = 0
The y-distance between H and J is = 9 - (-3) = 9 + 3 = 12
(1/3) of 12 = 4
(-3) + 4 = -3 + 4 = 1
The coordinates of I are (0,1)
Noting that the distance from I to J is 2/3, so we could have calculated I as the point 2/3 away from J.
The distances are the same (12). (2/3) of 12 is 8.
8 - 8 = 0 (as before for x)
9 - 8 = 1 (as before for y)
(0,1) are the coordinates of I.
I am sure you can graph the points, H, I and J.
