Question

Plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.
$(-2,1),(-3,-1),(4,-4),(-4,4),(-4,\frac{3}{2})$

Short answer

The required graph is

And the coordinates$(-4,4),(-4,1.5),(-2,1)$lie in the 2nd Quadrant,$(-3,-1)$lies in the 3rd Quadrant and$(4,-4)$lies in the 4th quadrant.

Step-by-step solution

Step 1. Given Information

We are given the coordinates$(-2,1),(-3,-1),(4,-4),(-4,4),(-4,\frac{3}{2})$

Step 2. Graph

We will use the desmos graph calculator to plot the given coordinates in the rectangular system as follows,

Step 3. Explanation

Consider the coordinates $(-4,4),(-4,1.5),(-2,1)$, we can see that the $x$coordinate is negative and localid="1658322079793" $y$coordinate is positive which implies that the coordinates lie in 2^nd Quadrant.

Next, we will consider the coordinate $(-3,-1)$

we can see that the localid="1658322099176" $x$coordinate is negative and localid="1658322084715" $y$coordinate is also negative which implies that the coordinate lie in 3^rd Quadrant.

Further, we will consider the coordinate $(4,-4)$, we can see that the localid="1658322090327" $x$coordinate is positive and localid="1658322095266" $y$coordinate is negative which implies that the coordinate lie in 4^th Quadrant.