MHB Find "h" & "k" Given a,b,c,d,f,g: Method Explained

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To find the values of h and k given the integers a, b, c, d, f, and g, one can use vector equations based on the relationship $\vec{OA} + \vec{AB} + \vec{BD} = \vec{OD}$. This equation implies that the sum of the vectors from point O to A, from A to B, and from B to D must equal the vector from O to D. By breaking down the vectors into their components, one can derive the necessary equations to solve for h and k. The solution involves manipulating these vector equations to isolate h and k. Understanding the geometric interpretation of the vectors can also aid in visualizing the problem.
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Some directed line segments are given by:

View attachment 5397if a,b,c,d,f,g are given (integers), by what method can i use to find h and k? Thanks...
 

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It holds that $\vec{OA}+\vec{AB}+\vec{BD}=\vec{OD}$.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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