Using proportions, it is found that the coordinates of point C are given as follows: C(-7, -2).
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Point C divides the line segment OP into the ratio 3:5, hence the following equation is used to relate the points:
[tex]C - O = \frac{3}{8}(P - O)[/tex]
Then, for the x-coordinate:
[tex]x + 10 = \frac{3}{8}(-2 + 10)[/tex]
x + 10 = 3
x = -7
For the y-coordinate:
[tex]y + 8 = \frac{3}{8}(8 + 8)[/tex]
y + 8 = 6
y = -2
The coordinates of point C are given as follows: C(-7, -2).
More can be learned about proportions at https://brainly.com/question/24372153
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