Given: the coordinates of rhombus wxyz are w(0, 4b), x(2a, 0), y(0, −4b), and z(−2a, 0).
prove: the segments joining the midpoints of a rhombus form a rectangle.

as part of the proof, find the midpoint of wx

(−a, −2b)

(a, −2b)

(a, 2b)

Step-by-step explanation:

mid point of WX (say P)=((0+2a)/(2),(4b+0)/(2))=(a,2b)

mid point of XY (say Q)=((2a+0)/(2),(0-4b)/(2)=(a,-2b)

mid point of YZ (say R)=((0-2a)/(2),(-4b+0)/(2)=(-a,-2b)

mid point of WZ (say S)=((0-2a)/(2),(4b+0)/(2)=(-a,2b)

PQ=4b

QR=2a

RS=4b

WS=2a

PQ=RS

QR=WS

PR=QS

hence opposite sides are equal and diagonals are also equal.

so it is a rectangle.

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