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Question
Write the coordinates of each of the vertices of each polygon in Fig. 27.9.
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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).
RELATED QUESTIONS
Plot the following points on a graph sheet. Verify if they lie on a line
K(2, 3), L(5, 3), M(5, 5), N(2, 5)
State whether True or False. Correct those are false.
The coordinates of the origin are (0, 0).
The point where the two axes intersect is called the ______.
Match the ordinates of the points given in Column A with the items mentioned in Column B.
| Column A | Column B |
| (a) (7, 0) | (i) The ordinate is double the abscissa. |
| (b) (11, 11) | (ii) The ordinate is zero. |
| (c) (4, 8) | (iii) The ordinate is equal to the abscissa. |
| (d) (6, 2) | (iv) The abscissa is double the ordinate. |
| (e) (0, 9) | (v) The abscissa is triple the ordinate. |
| (f) (6, 3) | (vi) The abscissa is zero. |
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This graph shows a map of an island just off the coast of a continent. The point labelled B represents a major city on the coast. The distance between grid lines represents 1 km.
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(i) On a copy of the map, mark the point that is 3 km East and 5 km North of Point B and label it S. Is Point S in the water or on the island? Is Point S in the same place as Point A?
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(v) Give the coordinates of the point that is halfway between Points L and P.
(vi) List three points on the island with their x-coordinates greater than 8.
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Sonal and Anmol made a sequence of tile designs from square white tiles surrounding one square purple tile. The purple tiles come in many sizes. Three of the designs are shown below.
(a) Copy and complete the table
| Side Length of Purple Titles | 1 | 2 | 3 | 4 | 5 | 10 | 100 |
| Number of white Tiles in Border |
 |
 |
 |
(b) Draw a graph using the first five pairs of numbers in your table.
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