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