Answer:
(-2, 6)
Step-by-step explanation:
Since you want a 1 to 7 ratio, you want to divide the line into 2 parts, where one part has a length of 1 and the other has a length of 7. So the total length of the line is 8.
Start by looking at the difference in the X and Y coordinates.
X = | -4 - 12 | = | -16 | = 16
Y = | 7 - -1 | = | 8 | = 8
You could calculate the length of the line using pythagorian's theorem, but that's not needed. Simply use similar triangles. We have a right triangle with legs of length 16 and length 8. We want a similar triangle that is 1/8th as large (to get the desired 1 to 7 ratio). So divide both legs by 8, getting lengths of 16/8 = 2, and 8/8 = 1.
Now add those calculated offsets to point A.
A has an X coordinate of -4 and B has an X coordinate of 12 and the X coordinate for C must be between those limits. So calculate -4 + 2 = -2 to get the X coordinate for C.
The Y coordinate of A is 7 and the Y coordinate of B is -1. And since the Y coordinate must be between then, you have 7 - 1 = 6.
So the coordinates for C is (-2, 6)
