Chapter 1.1, Problem 14AYU

In Problems 15 and 16, plot each point in the $xy\text{-plane}$. Tell in which quadrant or on what coordinate axis each point lies.

16. (a) $A=\left(1,4\right)$

(b) $B=\left(-3,-4\right)$

(c) $C=\left(-3,\text{ 4}\right)$

(d) $D=\left(4,\text{ 1}\right)$

(e) $E=\left(0,\text{ 1}\right)$

(f) $F=\left(-3,\text{ 0}\right)$

To determine

To plot: The points on $xy\text{-plane}$ and find the quadrant.

Explanation of Solution

Given:

$\text{A}\left(1,4\right),\text{ B}\left(-3,-4\right),\text{ C}\left(-3,4\right),\text{ D}\left(4,1\right),\text{ E}\left(0,1\right),\text{ F}\left(-3,0\right)$

To locate the point $\text{A}\left(1,4\right)$, go 1 unit to the right of 0 along the x axis (horizontal line) and go 4 units straight up. We plot this point by placing a dot at this location. This point lies in the 1st quadrant.

To locate the point $\text{B}\left(-3,-4\right)$, go 3 units to the left of 0 and go 4 units straight down. We plot this point by placing a dot at this location. This point lies in the 3rd quadrant.

To locate the point $\text{C}\left(-3,4\right)$, go 3 units to the left of 0 along the x axis and go 4 units straight up. We plot this point by placing a dot at this location. This point lies in the 2nd quadrant.

To locate the point $\text{D}\left(4,1\right)$, go 4 units to the right of 0 along the x axis and go 1 unit straight up. We plot this point by playing a dot at this location. This point lies in the 1st quadrant.

To locate the point $\text{E}\left(0,1\right)$, go 1 unit straight above 0 and place a dot at this location. This point lies on the positive y axis.

To locate the point $\text{F}\left(-3,0\right)$, go 3 units to the left of 0 and place a dot at this location. This point lies on the negative x axis.