MHB Find the ratios of the areas of the four regions

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The discussion focuses on finding the area ratios of four regions formed in square ABCD by point M, the midpoint of side CD. It highlights that triangles MPC and APB are similar, which is crucial for determining the area ratios. Participants suggest using properties of similar triangles to derive the necessary ratios. The conversation emphasizes the importance of justification in the calculations to ensure accuracy. Overall, the goal is to clearly establish the area ratios of ∆MPC, ∆BPC, ∆APB, and quadrilateral APMD.
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In square ABCD point M is the midpoint of side CD. Find the ratios of the areas of the four regions (∆MPC, ∆BPC, ∆APB, and quadrilateral APMD) that are formed. Justify your result.View attachment 8047
 

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Re: Having a difficult time figuring out how to solve this

Hello, and welcome to MHB! (Wave)

I think my first step would be to explain how $\triangle MPC$ and $\triangle APB$ are similar, from which we can determine the ratio of their areas...
 
Thread 'erroneously finding discrepancy in transpose rule'

Thread 'erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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