Q.2 - Intermediate Algebra

Question

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

a) $\left(-2,-3\right)$

b) $\left(3,-3\right)$

c) $\left(-4,1\right)$

d) $\left(4,-1\right)$

e) $\left(\frac{3}{2},1\right)$

Step-by-Step Solution

Answer

The plot of the points on the rectangular coordinate system is given by:

$\left(-2,-3\right)$ lies in Quadrant III. $\left(3,-3\right),\left(4,-1\right)$ lie in Quadrant IV. $\left(-4,1\right)$ lies in Quadrant II. $\left(\frac{3}{2},1\right)$ lies in Quadrant I.

Step 1. Given Information

Given points are $\left(-2,-3\right),\left(3,-3\right),\left(-4,1\right),\left(4,-1\right),\left(\frac{3}{2},1\right)$

The points are to be plotted on the rectangular coordinate system and the quadrant in which the point is located is to be identified.

Step 2. Plotting the points

The point $\left(-2,-3\right)$ is located 2 units left of the origin and 3 units below origin.

Locating the other points similarly, the plot of the points is

Step 3. Identifying the quadrant

For a point when both the x and y coordinates are positive, the point lies in Quadrant I

For a point when the x-coordinate is negative and the y-coordinate is positive, the point lies in Quadrant II.

For a point when both the x and y coordinates are negative, the point lies in Quadrant III

For a point when the x-coordinate is positive and the y-coordinate is negative, the point lies in Quadrant IV.

If the x-coordinate is 0, the point lies on y-axis.

If the y-coordinate is 0, the point lies on x-axis.

For $\left(-2,-3\right)$, both the coordinates are negative. Hence the point lies in Quadrant III.

For $\left(3,-3\right),\left(4,-1\right)$, the x coordinate is positive and the y coordinate is negative. Hence the points lie in Quadrant IV.

For $\left(-4,1\right)$, the x-coordinate is negative and the y-coordinate is positive. Hence the point lies in Quadrant II.

For $\left(\frac{3}{2},1\right)$, both the coordinates are positive. Hence the point lies in Quadrant I.

Step 4. Conclusion

The plot of the points is

$\left(-2,-3\right)$ lies in Quadrant III. $\left(3,-3\right),\left(4,-1\right)$ lie in Quadrant IV. $\left(-4,1\right)$ lies in Quadrant II. $\left(\frac{3}{2},1\right)$ lies in Quadrant I.