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3 years ago

Polygon WXYZ has vertices W (-1.5, 1.5)X(6, 1.5) Y(6, -4.5) and Z (-1.5, -4.5 )is WXYZ a rectangle

Mathematics

1 answer:

QveST [7]3 years ago

3 0

Answer:

WXYZ is a rectangle

Step-by-step explanation:

∵ W = (-1.5 , 1.5) , X = (6 , 1.5)

∴ WX is a horizontal segment ⇒ same y-coordinates

∴ WX = 6 - -1.5 = 6 + 1.5 = 7.5 units ⇒ (1)

∵ Y = (6 , -4.5) , X = (6 , 1.5)

∴ XY is a vertical segment ⇒ same x-coordinates

∴ XY = 1.5 - -4.5 = 1.5 + 4.5 = 6 units ⇒ (2)

From (1) and (2) WX ⊥ XY

∵ Y = (6 , -4.5) , Z = (-1.5 , -4.5)

∴ YZ is a horizontal segment ⇒ same y-coordinates

∴ YZ = 6 - -1.5 = 6 + 1.5 = 7.5 units ⇒ (3)

From (1) and (3)

∴ WX // YZ and WX = YZ

∴ WXYZ is a rectangle ⇒ 2 opposite sides are parallel and equal

and 2 adjacent sides are ⊥

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