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

Solution:

From the figure, we have:

In polygon 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 units and YZ is equal to 2 units. 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.

Also, draw perpendiculars DF, AE, CF and BE from A, B, C and D on the y-axis.

Now, from the figure:

DF = 3 units and DG = 3 units

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

AE = 4 units and AH = 5 units

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

CF = 6 units and CI = 3 units

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

BE = 7 units and BJ = 5 units

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

In polygon PQR:

Draw perpendiculars PJ, QK and RK from P, Q and R on the x-axis.

Also, draw perpendiculars PW, QE and RF from P, Q and R on the y-axis.

Now, from the figure:

PW = 7 units and PJ = 4 units

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

QE = 9 units and QK = 5 units

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

RF = 9 units and RK = 3 units

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