Question

3. Square SQRE has coordinates S(2, 2) Q (5,2)R (5. – 1). Find the coordinates of E. I gotta turn it in tomorrow

Answer 1

Given:

Square SQRE has coordinates S(2, 2) Q (5,2), and R (5. – 1).

To find:

The coordinates of E.

Step-by-step explanation:

Let (x, y) be the coordinates of E.

Using the midpoint formula,

`p=((x_1+x_2)/(2),(y_1+y_2)/(2))`

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.

`\begin{gathered} Midpoint\text{ of SR = Midpoint of QE} \\ ((2+5)/(2),(2-1)/(2))=((5+x)/(2),(2+y)/(2)) \\ ((7)/(2),(1)/(2))=((5+x)/(2),(2+y)/(2)) \end{gathered}`

Equating the coordinates we get,

`\begin{gathered} (7)/(2)=(5+x)/(2) \\ 7=5+x \\ x=2 \\ (1)/(2)=(2+y)/(2) \\ 1=2+y \\ y=-1 \end{gathered}`

Therefore, the coordinate of E is (2, -1).

Final answer:

The coordinate of E is (2, -1).