Given:
Square SQRE has coordinates S(2, 2) Q (5,2), and R (5. – 1).
To find:
The coordinates of E.
Explanation:
Let (x, y) be the coordinates of E.
Using the midpoint formula,
[tex]p=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]As we know,
The diagonals of the square are intersected by its midpoint.
So, the Midpoint of SR and QE is the same in a given square SQRE.
[tex]\begin{gathered} Midpoint\text{ of SR = Midpoint of QE} \\ (\frac{2+5}{2},\frac{2-1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \\ (\frac{7}{2},\frac{1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \end{gathered}[/tex]Equating the coordinates we get,
[tex]\begin{gathered} \frac{7}{2}=\frac{5+x}{2} \\ 7=5+x \\ x=2 \\ \frac{1}{2}=\frac{2+y}{2} \\ 1=2+y \\ y=-1 \end{gathered}[/tex]Therefore, the coordinate of E is (2, -1).
Final answer:
The coordinate of E is (2, -1).
