Using proportions, it is found that:
- The coordinates of point E are (3,0).
- The coordinates of point H are (3.45, 5.4).
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Point E divides FG in the ratio 3:4, hence:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
This is used to find both the x and y coordinates.
For the x-coordinate, we have that:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
[tex]x - 3.75 = \frac{3}{7}(2 - 3.75)[/tex]
x - 3.75 = -0.75.
x = 3.
For the y-coordinate:
[tex]E - F = \frac{3}{7}(G - F)[/tex]
[tex]y - 9 = \frac{3}{7}(-12 - 9)[/tex]
y - 9 = -9
y = 0.
The coordinates of point E are (3,0).
Point H divides FE in the ratio 2:3, hence:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
This is used to find both the x and y coordinates.
For the x-coordinate, we have that:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
[tex]x - 3.75 = \frac{2}{5}(3 - 3.75)[/tex]
x - 3.75 = -0.3.
x = 3.45.
For the y-coordinate, we have that:
[tex]H - F = \frac{2}{5}(E - F)[/tex]
[tex]y - 9 = \frac{2}{5}(0 - 9)[/tex]
y - 9 = -3.6
y = 5.4.
The coordinates of point H are (3.45,5.4).
More can be learned about proportions at https://brainly.com/question/24372153
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