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?
+2446 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.
