Answer:
(5, 7.8)
Step-by-step explanation:
There are several ways to solve this problem, but all of them involve similar triangles and ratios.
See the attached image.
The horizontal distance between points D and E is 11 - 1 = 10. If a segment 10 units long is divided in the ratio 2:3 (as shown by the two smaller segments of length a and b), then
[tex]\frac{a}{b}=\frac{2}{3}\\\frac{a}{a+b}=\frac{2}{2+3}\\\frac{a}{10}=\frac{2}{5}[/tex]
"Cross-multiply" to get
5a = 20
a = 4
To get the x-coordinate of point G, add 4 to 1, the x-coordinate of D.
The x-coordinate of G is 1 + 4 = 5.
The same idea can be used on the second coordinate of G.
The vertical distance from D to E is 15 - 3 = 12.
[tex]\frac{a}{b}=\frac{2}{3}\\\frac{a}{a+b}=\frac{2}{2+3}\\\frac{a}{12}=\frac{2}{5}[/tex]
5a = 24
a = 24/5 = 4.8
The y=coordinate of G is 3 + 4.8 = 7.8
