COORDINATE GEOMETRY - Q&A
Exercise 3.1
1. How will you describe the position of a table lamp on your study table to another person?
To describe the position of a table lamp on the study table, we can use the concept of coordinates.
1. Consider the table top as a plane surface and the two perpendicular edges of the table (say the bottom edge and the left edge) as the x-axis and y-axis respectively.
2. Measure the distance of the lamp from the longer edge (let's say it is 25 cm) and from the shorter edge (let's say it is 30 cm).
3. We can then describe the position of the lamp as (25, 30) or (30, 25) depending on which edge we consider as the x-axis.
[Image of coordinates of a point on a plane]
So, the position is uniquely defined by these two distances.
2. (Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross - streets can be referred to as (4, 3).
There is only one cross-street that can be referred to as (4, 3). This is the intersection of the 4th street running North-South and the 3rd street running East-West.
(ii) how many cross - streets can be referred to as (3, 4).
There is only one cross-street that can be referred to as (3, 4). This is the intersection of the 3rd street running North-South and the 4th street running East-West.
Exercise 3.2
1. 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?
The horizontal line is called the x-axis and the vertical line is called the y-axis.
[Image of cartesian plane x and y axis]
(ii) What is the name of each part of the plane formed by these two lines?
Each part of the plane formed by these two lines is called a quadrant. There are four quadrants: I, II, III, and IV.
[Image of quadrants in cartesian plane]
(iii) Write the name of the point where these two lines intersect.
The point where the x-axis and y-axis intersect is called the origin, denoted by O(0, 0).
2. See Fig. 3.14, and write the following:
(i) The coordinates of B.
The point B is at a distance of -5 units along the x-axis and 2 units along the y-axis.
So, the coordinates of B are (-5, 2).
(ii) The coordinates of C.
The point C is at a distance of 5 units along the x-axis and -5 units along the y-axis.
So, the coordinates of C are (5, -5).
(iii) The point identified by the coordinates (-3, -5).
Looking at the graph, the point with x-coordinate -3 and y-coordinate -5 is E.
So, the point is E.
(iv) The point identified by the coordinates (2, -4).
Looking at the graph, the point with x-coordinate 2 and y-coordinate -4 is G.
So, the point is G.
(v) The abscissa of the point D.
The abscissa is the x-coordinate. Point D is at x = 6.
So, the abscissa of point D is 6.
(vi) The ordinate of the point H.
The ordinate is the y-coordinate. Point H is at y = -3.
So, the ordinate of point H is -3.
(vii) The coordinates of the point L.
Point L lies on the y-axis at y = 5. Its x-coordinate is 0.
So, the coordinates of L are (0, 5).
(viii) The coordinates of the point M.
Point M lies on the x-axis at x = -3. Its y-coordinate is 0.
So, the coordinates of M are (-3, 0).