A large trapezium made up of four equal trapeziums:

Find the coordinates of the vertices of all these trapeziums.

Draw this picture in GeoGebra.

Since, the four trapeziums are equal

OA = AB

∴ A bisects OB

OB = 8

∴ OA = 4

∴ coordinates of A = (4,0)[A is on X axis]

And coordinates of B = (8,0)[B is on X axis]

BC is parallel to Y – axis,

∴ X coordinate will remain constant

∴ X coordinate of C = 8

Since all four trapeziums are equal,

BC = OA = 4 = Y coordinate of C

∴ Y coordinate of C = 4

∴ coordinates of C = (8,4)

AF = GD[All trapeziums are equal]

AF + GD = BC = 4

∴ AF = GD = 2

AF = Y coordinate of F = 2

Line AF is parallel to Y – axis,

∴ X coordinate will remain constant.

∴ X coordinate of F = 4

∴ coordinates of F = (4,2)

Line FG is parallel to X – axis,

∴ Y coordinate will remain constant

∴ Y coordinate of G = 2

FG = DC[All trapeziums are equal]

FG + DC = AB = 4

∴ FG = DC = 2

X coordinate of G = X coordinate of F + FG

= 4 + 2 = 6

∴ coordinates of G = (6,2)

CD is parallel to X – axis,

∴ Y coordinate will remain constant

∴ Y coordinate of D = 4

GD is parallel to Y – axis,

∴ X coordinate will remain constant

∴ X coordinate of D = 6

∴ coordinates of D = (6,4)

CI is parallel to X axis

∴ Y coordinate will remain constant

∴ Y coordinate of I = 4

AI us parallel to Y – axis,

∴ X coordinate will remain constant

∴ X coordinate of I = 4

∴ coordinates of I = (4,4)

OH and HI will be equal in length and will be at equal angles with X axis[All trapeziums are equal]

∴ H will be the midpoint of OI

∴ H will be the mid point of(0,0) and (4,4)

∴ coordinates of H = (2,2)