How will you describe the position of a table lamp on your study table to another person?
Answer
Steps :
Consider the lamp as a point and table as a plane.
Let ABCD be the top view of table and E be the position of lamp.
Let AD be y-axis and CD be x-axis.
From point E draw EF ⊥ AD and EG ⊥ CD.
Measure EF = 25 units (let) and EG = 30 units (let).
The distance of the point from the x-axis and y-axis is x and y respectively, so the coordinates of table lamp will be (x, y).
E(x, y) = (EF, EG) = (25, 30).
Hence, position of lamp on table can be described by coordinates (25, 30).
(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).
(ii) How many cross-streets can be referred to as (3, 4).
Answer
Steps of construction :
Consider NS as y-axis and EW as x-axis.
Draw 5 streets parallel to both the axis.
Suppose x no. street parallel to y-axis crosses y no. street parallel to x-axis, so the cross street will be referred as (x, y).
Mark the points (4, 3) and (3, 4).
Both the cross-streets are marked in the figure above. They are uniquely found because of the two reference lines we have used for locating them.
(i) From figure,
Only one street can be referred as (4, 3).
(ii) From figure,
Only one street can be referred as (3, 4).
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?
(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
(i) x-axis and y-axis.
(ii) Quadrants.
(iii) The origin.
See figure, 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
(i) The coordinates of point B are (–5, 2).
(ii) The coordinates of point C are (5, –5).
(iii) The point identified by the coordinates (–3, –5) is E.
(iv) The point identified by the coordinates (2, –4) is G.
(v) The abscissa of the point D is 6.
(vi) The ordinate of the point H is -3.
(vii) The coordinates of the point L is (0, 5).
(viii) The coordinates of the point M is (-3, 0).