A( 1, 2 ),B( 3,4) are opposite vertices of square,  perpendicular distance from  (−2,3) to other diagonal ( not passing through  A,B ) of the square is

Mid point of AB=(2, 3) = centre of the squareSlope of (AB)=1Slope of (CD)=−1Equation of CD¯⇒y−3=−1(x−2) (passes through the centre of the square)⇒x+y−5=0Perpendicular distance from (−2,3) to x+y−5=0d=|−2+3−52|=|−42|=22