Let's first find the coordinates of I. The x-coordinate of I is -4 and the y-coordinate of I is -5.
Now, let's find the x-coordinate of G. Since the ratio of FG to FH is 1:2, the difference between the x-coordinates of G and F is 1/3 of the difference between the x-coordinates of H and F. So, the x-coordinate of G is:
x-coordinate of G = x-coordinate of F + (1/3)(x-coordinate of H - x-coordinate of F)
x-coordinate of G = (-7) + (1/3)(-4 - (-7))
x-coordinate of G = -7 + (1/3)(-3)
x-coordinate of G = -7 + (-1)
x-coordinate of G = -8
Next, let's find the y-coordinate of G. Since the ratio of FG to FH is 1:2, the difference between the y-coordinates of G and F is 1/3 of the difference between the y-coordinates of H and F. So, the y-coordinate of G is:
y-coordinate of G = y-coordinate of F + (1/3)(y-coordinate of H - y-coordinate of F)
y-coordinate of G = 4 + (1/3)(-5 - 4)
y-coordinate of G = 4 + (1/3)(-9)
y-coordinate of G = 4 + (-3)
y-coordinate of G = 1
Therefore, the coordinates of G are (-8, 1).
Given FH with coordinates F(-7,4) and HI(-4-5), if G lies on FI such that that the ratio of FG to FH is 1:2, find the coordinates of G
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