Plot the following ordered pairs in the same xy-plane. Tell in which quadrant or on what coordinate axis each point lies. A ( 7 , 0 ) , B ( − 2 , 6 ) ,C ( 8 , 4 ) , D ( 0 , − 9 ) , E ( − 5 , − 10 ) , F ( 6 , − 3 )

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Answer 1

Textbook Question

Chapter 8, Problem 1PCT

Plot the following ordered pairs in the same xy-plane. Tell in which quadrant or on what coordinate axis each point lies.

A ( 7 , 0 ) , B ( − 2 , 6 ) ,C ( 8 , 4 ) , D ( 0 , − 9 ) , E ( − 5 , − 10 ) , F ( 6 , − 3 )

Expert Solution & Answer

To determine

To plot: The given points in the xy-plane and obtain the coordinate axis where each points lies.

Answer to Problem 1PCT

The coordinate axes where the points A(7,0),B(−2,6),C(8,4),D(0,−9),E(−5,−10) and F(6,−3) lie are positive x-axis, second quadrant, first quadrant, negative y-axis, third quadrant and fourth quadrant, respectively.

Explanation of Solution

In general, any point P in the rectangular coordinate system is represented by the ordered pair (x,y), where x and y are said to be the x coordinate and y coordinate of the point P.

Recall that, x and y are positive in the first quadrant. In the second quadrant, x is negative and y is positive. In the third quadrant, both x and y are negative. And in the fourth quadrant, x is positive and y is negative.

The given points are, A(7,0),B(−2,6),C(8,4),D(0,−9),E(−5,−10) and F(6,−3).

Consider the point A(7,0). Here, the x coordinate is positive and the y coordinate is 0. So the point A(7,0) lies on Positive x-axis.

For the point B(−2,6), the x coordinate is negative and the y coordinate is positive. Thus, the point B(−2,6) lies in the second quadrant.

Similarly, for the point C(8,4), both x coordinate and y coordinate are positive. So, the point C(8,4) lies in the first quadrant.

For the point D(0,−9), the x coordinate is 0 and the y coordinate is negative. So, the point lies on the negative y-axis.

In the case of E(−5,−10), both x and y coordinates are negative. Thus, the point E(−5,−10) lies in the third quadrant.

For the point F(6,−3), the x coordinate is positive and the y coordinate is negative. So the point lies in the fourth quadrant.

Draw the graph and plot the points as shown below in Figure 1.

Elementary & Intermediate Algebra, Chapter 8, Problem 1PCT

From Figure 1, it is observed that the dark dots represents the given points A(7,0),B(−2,6),C(8,4),D(0,−9),E(−5,−10) and F(6,−3).

Thus, the coordinate axes where the points A(7,0),B(−2,6),C(8,4),D(0,−9),E(−5,−10) and F(6,−3) lie are positive x-axis, second quadrant, first quadrant, negative y-axis, third quadrant and fourth quadrant, respectively.

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