Answer:
x = 6 sqrt(3)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2+ x^2 = 12^2
36 + x^2 = 144
Subtract 36 from each side
x^2 = 144-36
x^2 =108
Take the square root of each side
sqrt(x^2) = sqrt(108)
x = sqrt(36*3)
x = 6 sqrt(3)
3:5 ratio mean there are 8 "parts" (3 + 5 = 8)
The distance between the x-coordinates is |-3 - 5| = 8.
So each "part" is 8/8 = 1 unit long in the x-direction.
You want I to be 3(1) = 3 units from D, so the x-coordinate of I is -3 + 3 = 0.
Same deal for y.
|2 - 5| = 3 is the distance between D and E
Each part is 3/8.
3(3/8) = 9/8
2 + 9/8 = 25/8
So the point I is (0, 25/8)