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6

Write the coordinates of each of the vertices of each polygon in Fig. 27.9.

In quadrilateral OXYZ,

O lies on the origin and the coordinates of the origin are (0, 0). So, the coordinates of O are (0, 0).

X lies on the *y*-axis. So, the *x*-coordinate is 0. Hence, the coordinate of X is (0, 2).

Also, YX is equal to 2 cm and YZ is equal to 2 cm. So, the coordinates of vertex Y are (2, 2).

Z lies on the *x*-axis. So, the *y*-coordinate is 0. Hence, the coordinates of Z are (2, 0).

In polygon ABCD,

Draw perpendiculars DG, AH, CI and BJ from A, B, C and D on the *x*-axis and DF, AE, CF and BE from A, B, C and D on the *y*-axis.

DF = 3 cm and DG = 3 cm

Therefore, the coordinates of D are (3, 3).

AE = 4 cm and AH = 5 cm

Therefore, the coordinates of A are (4, 5).

CF = 6 cm and CI = 3 cm

Therefore, the coordinates of C are (6, 3).

BE = 7 cm and BJ = 5 cm

Therefore, the coordinates of B are (7, 5).

In triangle PQR,

Draw perpendiculars PJ, QK and RK from P, Q and R on the *x*-axis and PW, QE and RF from P, Q and R on the *y*-axis.

PW = 7 cm and PJ = 4 cm

Therefore, the coordinates of P are (7, 4).

QE = 9 cm and QK = 5 cm

Therefore, the coordinates of Q are (9, 5).

RF = 9 cm and RK = 3 cm

Therefore, the coordinates of R are (9, 3).