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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
Locate the points:
(1, 3), (2, 3), (3, 3), (4, 3)
Decide which of the following statements is true and which is false. Give reasons for your answer.
The coordinates of the origin are (0, 0).
The following table gives the information regarding length of a side of a square and its area:
| Length of a side (in cm): | 1 | 2 | 3 | 4 | 5 |
| Area of square (in cm2): | 1 | 4 | 9 | 16 | 25 |
Draw a graph to illustrate this information.
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. |
Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.
(1, 2), (2, 4), (3, 6), (4, 8)
Explain the situations represented by the following distance-time graph.
The following is the time-distance graph of Sneha’s walking.
- When does Sneha make the least progress? Explain your reasoning.
- Find her average speed in km/hour.
