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If (7, 9) and (10, 2) are the coordinates of two opposite vertices of a square, what is the sum of the y-coordinates of the other two vertices?

 May 17, 2020
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The midpoint of (7,9) and (10,2) is located at the average of x- and y-coordinates of both vertices.

\(M=(x,\frac{9+2}{2})\\ M=(x,\frac{11}{2})\)

 

This midpoint is the same for the other two vertices of the square. Let's let the y-coordinates of the first unknown vertex be \(y_1\) and the second unknown vertex one be \(y_2\). Then, we would calculate the average of those vertices as follows:

 

\(\frac{y_1+y_2}{2}=\frac{11}{2}\\ y_1+y_2=11\)

 

Therefore, the sum of the y-coordinates of the other two vertices is 11.

 May 17, 2020

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