Prove the diagonals of the square with vertices P (0,4), Q (4,4), R (0,0) and S (4,0) are perpendicular bisectors of each other. Step 1: calculate the slope of the diagonals. The slope of diagonal PS is ____The slope of diagonal QR is ____ Step 2: calculate the midpoint of the diagonals The midpoint of PS is ___ Midpoint of QR is ___

The diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.Given information:The square with vertices P (0,4), Q (4,4), R (0,0) and S (4,0).It is required to prove that the diagonals of the given square are perpendicular bisectors.First, calculate the slope of the diagonals.The slope of diagonal PS will be,[tex]m = \dfrac{0-4}{4-0}\\m = -1[/tex]So, the slope of diagonal PS is -1. The slope of diagonal QR will be,[tex]m' = \dfrac{0-4}{0-4}\\m' = 1[/tex]So, the slope of diagonal QR is 1.From the slope of the diagonals, the diagonals are perpendicular because the product of slope is -1.Now, it is required to find the mid-point of the diagonals.The midpoint of PS will be,[tex](x,y)=(\dfrac{0+4}{2},\dfrac{4+0}{2})=(2,2)[/tex]Midpoint of QR will be,[tex](x,y)=(\dfrac{4+0}{2},\dfrac{4+0}{2})=(2,2)[/tex]So, the midpoint of both the diagonals is also same.Therefore, it can be said that the diagonals are perpendicular because the product of their slope is -1, and their midpoint is same (2,2). Hence, it is proved that the diagonals of the given square are perpendicular bisectors of each other.For more details, refer to the link: