Ex - 3.3
Question 1. In which quadrant or on which axis do each of the points (-2,4), (3,-1), (-1,0), (1,2) and (-3,-5) lie? Verify your answer by locating them on the Cartesian plane.
Solution
(i) The point (-2,4) lies in IInd quadrant in Cartesian plane as for point (-2,4), x coordinate is negative and y coordinate is positive.
(ii) The point (3,-1) lies in IVth quadrant in Cartesian plane because for point (3,-1) , x coordinate is positive and y coordinate is negative.
(iii) The point (-1,0) lies on negative x-axis because for point (-1,0) the value of y coordinate is zero and the value of x coordinate is negative.
(iv) The point (1,2) lies in Ist quadrant as for point (1,2) both x and y are positive
(v) The point (-3,-5) lies in the IIIrd quadrant in Cartesian plane as for point (-3,-5) both x and y are negative.
Now let's plot each of the above points on the coordinate plane.
Concept Insight:- The coordinates of a point are of the form (+,+) in the first quadrant, (-,+) in the second quadrant, (-.-) in the third quadrant and (+,-) in the fourth quadrant, where + denotes a positive real number and - denotes a negative real number. The coordinates of any point on the x axis has y coordinate as zero and for a point on y axis x coordinate is zero.
For plotting the points let say (3,4) start from the origin first move 3 units along positive x axis and then from this marked position move 4 units along positive y axis.
Question 2. Plot the point (x, y) given in the following table on the plane, choosing suitable units of distance on the axis.
Question 1. In which quadrant or on which axis do each of the points (-2,4), (3,-1), (-1,0), (1,2) and (-3,-5) lie? Verify your answer by locating them on the Cartesian plane.
Solution
(i) The point (-2,4) lies in IInd quadrant in Cartesian plane as for point (-2,4), x coordinate is negative and y coordinate is positive.
(ii) The point (3,-1) lies in IVth quadrant in Cartesian plane because for point (3,-1) , x coordinate is positive and y coordinate is negative.
(iii) The point (-1,0) lies on negative x-axis because for point (-1,0) the value of y coordinate is zero and the value of x coordinate is negative.
(iv) The point (1,2) lies in Ist quadrant as for point (1,2) both x and y are positive
(v) The point (-3,-5) lies in the IIIrd quadrant in Cartesian plane as for point (-3,-5) both x and y are negative.
Now let's plot each of the above points on the coordinate plane.
Concept Insight:- The coordinates of a point are of the form (+,+) in the first quadrant, (-,+) in the second quadrant, (-.-) in the third quadrant and (+,-) in the fourth quadrant, where + denotes a positive real number and - denotes a negative real number. The coordinates of any point on the x axis has y coordinate as zero and for a point on y axis x coordinate is zero.
For plotting the points let say (3,4) start from the origin first move 3 units along positive x axis and then from this marked position move 4 units along positive y axis.
Question 2. Plot the point (x, y) given in the following table on the plane, choosing suitable units of distance on the axis.
x
|
-2
|
-1
|
0
|
1
|
3
|
y
|
8
|
7
|
-1.25
|
3
|
-1
|
Solution
The given points are plotted on the Cartesian plane as below:
Concept Insight: The coordinates of a point (x,y) is such that its distance from y axis along the positive x axis is x units and the distance of the point from x axis along the y axis is y units. To locate such point we need to start from origin, count x units along x axis and then further move y units along y axis.
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