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.

$\text{A}(7,0),\text{B}\left(-2,6\right)\text{,C}\left(8,4\right),\text{D}\left(0,-9),\text{E}\left(-5,-10\right),\text{F}(6,-3\right)$

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 $A\left(7,0\right),B\left(-2,6\right),C\left(8,4\right),D\left(0,-9\right)\text{,}E\left(-5,-10\right)\text{ and }F\left(6,-3\right)$ 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 $\left(x,y\right)$, 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, $A\left(7,0\right),B\left(-2,6\right),C\left(8,4\right),D\left(0,-9\right)\text{,}E\left(-5,-10\right)\text{ and }F\left(6,-3\right)$.

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

For the point $B\left(-2,6\right)$, the x coordinate is negative and the y coordinate is positive. Thus, the point $B\left(-2,6\right)$ lies in the second quadrant.

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

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

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

For the point $F\left(6,-3\right)$, 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.

From Figure 1, it is observed that the dark dots represents the given points $A\left(7,0\right),B\left(-2,6\right),C\left(8,4\right),D\left(0,-9\right)\text{,}E\left(-5,-10\right)\text{ and }F\left(6,-3\right)$.

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