Q1. Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
Answer (1)(i). The horizontal line is called the x-axis and the vertical line is called the y-axis.
(ii) What is the name of each part of the plane formed by these two lines?
Answer (1)(ii). Each part is called a quadrant. The axes divide the plane into four quadrants (numbered I, II, III, IV).
(iii) Write the name of the point where these two lines intersect.
Answer (1)(iii). The point of intersection is the origin, denoted by O, and its coordinates are (0, 0).
Q2. (Refer to Fig. 3.14) 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 (2) — method and how to get the answers
I can’t reliably read the small graphical labels of Fig. 3.14 from the text snippet alone, so rather than guessing values, here is a short, foolproof method you (or I) should use to read off each requested item from the figure:
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To read the coordinates of any point (x, y):
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Move horizontally from the origin along the x-axis to the vertical line through the point — the signed distance from the y-axis is the x-coordinate (abscissa).
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Move vertically from the origin along the y-axis to the horizontal line through the point — the signed distance from the x-axis is the y-coordinate (ordinate).
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Put them together as (x, y).
(Positive directions are right for x and up for y; left and down are negative.)iemh103
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To locate the point identified by a pair (a, b): go to x = a (along the x-axis), then to y = b (along the y-axis). The intersection is the point with coordinates (a, b).
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The abscissa of a point is its x-coordinate (the horizontal signed distance from the y-axis).
The ordinate of a point is its y-coordinate (the vertical signed distance from the x-axis).