Question

Fill in the blanks according to coordinate system:
(i) The interior of $\angle XOY$ is called _____ quadrant.
(ii) The interior of $\angle YOX'$ is called _____ quadrant.
(iii) The interior of $\angle XOY'$ is called _____ quadrant.
(iv) The interior of $\angle Y'OX'$ is called _____ quadrant.
(v) Abscissa of (3,5) is _____
(vi) A point whose x coordinate is negative and y coordinate is positive lies in the _____ quadrant.

Answer 1

Hint: In this question, we have to first understand the coordinate system and then we will be able to answer our questions. We will draw a Cartesian plane and then analyze the plane to get our answer.

Complete step by step answer:
Here, let us first understand the coordinate system and the Cartesian plane. In the Cartesian plane, we have two axis, x axis and y axis which are perpendicular to each other. These axes cut each other at origin O and form four quadrants. The x axis is horizontal and y axis is vertical. Numbers written as x axis right side to the y axis are positive numbers whereas number on left side are the negative number. Similarly, the number on y-axis which is above x axis are positive and number on y-axis which is below x axis are negative. Any number in the plane is written in the form (x,y). Here, x is called abscissa and y is called the ordinate. Let us look at the Cartesian plane and label it according to standard notation.

Let us move to our question and use this diagram to answer them:
(i) The interior of $\angle XOY$ is called _____ quadrant.
As we can see from our plane, we have four quadrants. Positive x axis marked as X and the negative x axis is marked as X'. Similarly, the positive y axis is marked as Y and negative y axis is marked as Y'. From diagram, $\angle XOY$ lies in first quadrant. Therefore, the interior of $\angle XOY$ is called first quadrant.
(ii) The interior of $\angle YOX'$ is called _____ quadrant.
From diagram, we can see that $\angle YOX'$ lies in second quadrant. Therefore, the interior of $\angle YOX'$ is called second quadrant.
(iii) The interior of $\angle XOY'$ is called _____ quadrant.
From diagram, we can see that, $\angle XOY'$ lies in fourth quadrant. Therefore, the interior of $\angle XOY'$ is called fourth quadrant.
(iv) The interior of $\angle Y'OX'$ is called _____ quadrant.
From diagram, we can see that, $\angle Y'OX'$ lies in third quadrant. Therefore, the interior of $\angle Y'OX'$ is called the third quadrant.
(v) Abscissa of (3,5) is _____
We know for any coordinate point (x,y),x is called abscissa and y is called ordinate. So here, abscissa will be 3.
(vi) A point whose x coordinate is negative and the y coordinate is positive lies in _____ quadrant.
From the diagram, we can see that, when x is negative it is either the second quadrant or third quadrant. If y coordinate is positive then it is in the second quadrant. Hence, a point whose x coordinate is negative and y coordinate is positive lies in the second quadrant.
Note:
Students should know, the way quadrants are written in Cartesian plane. They should know that, point of type (x,y) lies in first quadrant, (-x,y) lies in second quadrant, (-x,-y) lies in third quadrant and (x,-y) lies in the fourth quadrant.