1How will you describe the position of a table lamp on your study table to another person?
Answer & Reference:
To describe the position of a table lamp, we need two independent pieces of information:
Its distance from the left edge of the table (say, x cm)
Its distance from the front (or bottom) edge of the table (say, y cm)
Thus, the position can be represented as an ordered pair (x, y). (Reference: Page 53, Section 3.1, Activity 1)
2(Street Plan): A city has two main roads crossing at the centre—one along North-South and the other along East-West. Other streets run parallel to these and are 200 m apart. There are 5 streets in each direction. Using 1 cm = 200 m, draw a model. A cross-street is referred to as (2, 5) if the 2nd North-South street meets the 5th East-West street. Using this convention, find:
(i) How many cross-streets can be referred to as (4, 3)?
(ii) How many cross-streets can be referred to as (3, 4)?
Answer & Reference:
(i) Only one cross-street can be referred to as (4, 3).
(ii) Only one cross-street can be referred to as (3, 4). Explanation: Each ordered pair (a, b) corresponds to a unique intersection point of the a-th North-South street and b-th East-West street. Hence, each pair identifies exactly one cross-street. (Reference: Page 54, Exercise 3.1, Question 2)
3Write the answer of each of the following questions:
(i) What is the name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
Answer & Reference:
(i) Horizontal line: x-axis; Vertical line: y-axis
(ii) Each part is called a quadrant
(iii) The point of intersection is called the origin (Reference: Page 59–60, Section 3.2)
4See Fig. 3.14, and write the following:
(i) The coordinates of B.
(ii) The coordinates of C.
(iii) The point identified by the coordinates (–3, –5).
(iv) The point identified by the coordinates (2, –4).
(v) The abscissa of the point D.
(vi) The ordinate of the point H.
(vii) The coordinates of the point L.
(viii) The coordinates of the point M.
Answer & Reference:
Based on Fig. 3.14 (Page 60):
Coordinates of B: (–5, 2)
Coordinates of C: (5, –5)
Point (–3, –5): E
Point (2, –4): G
Abscissa of D: 6
Ordinate of H: –3
Coordinates of L: (0, 5)
Coordinates of M: (–3, 0)
5What are the coordinates of the origin?
Answer & Reference:
The coordinates of the origin are (0, 0) because it lies at zero distance from both axes. (Reference: Page 63, Point 9 in Summary)
6What are the coordinates of a point lying on the x-axis?
Answer & Reference:
Any point on the x-axis has coordinates of the form (x, 0), since its perpendicular distance from the x-axis is zero. (Reference: Page 62, Example 2 and Summary Point 8)
7What are the coordinates of a point lying on the y-axis?
Answer & Reference:
Any point on the y-axis has coordinates of the form (0, y), since its perpendicular distance from the y-axis is zero. (Reference: Page 62, Example 2 and Summary Point 8)
8In which quadrant do the following points lie?
(i) (3, 4)
(ii) (–2, 5)
(iii) (–4, –3)
(iv) (5, –2)
Answer & Reference:
Based on sign conventions (Page 63, Fig. 3.13 and Summary Point 10):
Point
Signs
Quadrant
(3, 4)
(+, +)
I
(–2, 5)
(–, +)
II
(–4, –3)
(–, –)
III
(5, –2)
(+, –)
IV
9Define abscissa and ordinate.
Answer & Reference:
Abscissa: The x-coordinate of a point; its perpendicular distance from the y-axis measured along the x-axis.
Ordinate: The y-coordinate of a point; its perpendicular distance from the x-axis measured along the y-axis.
(Reference: Page 60, Section 3.2)
10Are the points (x, y) and (y, x) the same? Explain.
Answer & Reference:
No, (x, y) ≠ (y, x) unless x = y. The order matters: the first number is always the x-coordinate (abscissa), and the second is the y-coordinate (ordinate).
Example: (3, 4) and (4, 3) are different points. (Reference: Page 63, Summary Point 11)
11Illustrate the Cartesian plane with labeled quadrants and axes.
Answer & Reference:
Below is the standard Cartesian plane as described in Fig. 3.9 (Page 59):