Question

the quadrilateral abcd is a square. if the center of a square could be defined as the midpoint of one of its diagonals, what is the center of the square shown?
a. $(1,-1)$
b. $(-0.5,1)$
c. $(-1,1)$
d. $(-1.5,0.5)$

Explanation:

Step1: Find coordinates of diagonal endpoints

Assume diagonal \(AC\). From the graph, \(A(-5, 3)\) and \(C(3, -1)\).

Step2: Use mid - point formula

The mid - point formula is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
For \(x\) - coordinate: \(\frac{-5+3}{2}=\frac{-2}{2}=-1\).
For \(y\) - coordinate: \(\frac{3+( - 1)}{2}=\frac{2}{2}=1\).

Answer:

C. \((-1,1)\)