Find the side of the square with vertical and horizontal sides inscribed in the region representing the solution of the system left brace Start 2 By 1 Matrix 1st Row 1st Column y less than minus one half x squared plus 2 2nd Row 1st Column y greater than one half x squared minus 2 EndMatrix

Required side of the squire is , correct upto four desimal places.

Step-by-step explanation:

Given two inequalities are,

which are reflexions of each other across the axis. And the square is inscribed within it. Since by symmetry, vertices of the  square lies on the lines,

and . We only have to find length of any one side of the squire.

To find , substitute in we get,

Since and from , , and thus,

Similarly by substitute and we will get,  

And thus, , correct upto four desimal places.

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

hard

step-by-step explanation: