Question

Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), YO, -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 XY

Answer 1

∴ MNOP is Rectangle

midpoint of XY (N) : (a , - 2b)

Explanation:

W (0 , 4b) X ( 2a , 0) Y (0 , -4b) Z (-2a , 0)

M (midpoint of WX) : ( (0 + 2a)/2 , (4b + 0)/2) i. e. (a , 2b)

N (midpoint of XY) : ( (2a + 0)/2 , (0 - 4b)/2) i. e. (a , - 2b)

O (midpoint of YZ) : ( (0 - 2a)/2 , (- 4b + 0)/2) i. e. (- a , - 2b)

P (midpoint of ZW) : ( (0 - 2a)/2 , (4b + 0)/2) i. e. (- a , 2b)

MN: length = 2b + 2b = 4b MN segment perpendicular to x axis (slope undefined)

NO: length = a + a = 2a NO segment parallel to x axis (slope = 0)

OP: length = 2b + 2b = 4b OP segment perpendicular to x axis (slope undefined)

PM: length = a + a = 2a NO segment parallel to x axis (slope = 0)

MN = OP and MN // OP and MN ⊥ PM

NO = PM and NO // PM and NO ⊥ OP

∴ MNOP is Rectangle

midpoint of XY (N) : (a , - 2b)

please draw graph to prove