The coordinates of point F are (3.75, -2.5), and the coordinates of point G are (-0.75 , -3)
How to determine the coordinates of F and G?
The coordinates are given as:
A(-3,-1)
C-3,-3)
B(6,-3)
The diagram that completes the question is added as an attachment.
From the attached diagram, we have:
- Point G ⇒ m : n = 1 : 3 between C and B
- Point F ⇒ m : n = 3 : 1 between A and B
The vertices of the points are calculated using:
[tex](x,y) = \frac{1}{m + n} * (mx_2 + nx_1, my_2 + ny_1)[/tex]
So, we have:
[tex]G = \frac{1}{1 + 3} * (1 * 6 + 3 * -3 , 1 * -3 + 3 * -3)[/tex]
Evaluate
G = (-0.75 , -3)
Also, we have:
[tex]F = \frac{1}{3 + 1} * (3 * 6 + 1 * -3 , 3 * -3 + 1 * -1)[/tex]
Evaluate
F = (3.75, -2.5)
Hence, the coordinates of point F are (3.75, -2.5), and the coordinates of point G are (-0.75 , -3)
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