Question

Which quadrant does $\left( { - 1, - 2} \right)$ lie?

Answer 1

In this question, we have to plot the for the given point on the graph and check in which quadrant it lies. Here we have a value of x axis and y axis. They have given only one value of x and y. Hence by considering the points we plot it on the graph. Then by the definition and properties of quadrants we can check the quadrants in the graph both of the x or y values will be negative.

Complete answer:
A quadrant is one of the four sections on a Cartesian plane. Each quadrant includes a combination of positive and negative values for x and y.

There are four graph quadrants that make up the Cartesian plane. Each graph quadrant has a distinct combination of positive and negative values.
Quadrant I: The first quadrant is in the upper right-hand corner of the plane. Both x and y have positive values in this quadrant.
Quadrant II: The second quadrant is in the upper left-hand corner of the plane. X has negative values in this quadrant and y has positive values.
Quadrant III: The third quadrant is in the bottom left corner. Both x and y have negative values in this quadrant.
Quadrant IV: The fourth quadrant is in the bottom right corner. X has positive values in this quadrant and y has negative values.

Consider, the given question:
We need to find the quadrant which $\left( { - 1, - 2} \right)$ lie.
Here we have a point, usually the point is generally represented as $(x,y)$. The first term represents the x value and the second term represents the y value.
In $\left( { - 1, - 2} \right)$ when the x value is $- 1$, then the value of y is $- 2$. From the origin of a graph we have to move $1$ step left side along the x-axis and then $2$ steps move downwards along the y-axis from where x point is located.
Therefore, the graph for the point $\left( { - 1, - 2} \right)$ is plotted as shown below:

Hence, the point $\left( { - 1, - 2} \right)$ lies in the third quadrant because both x and y values are negative.

Note: A graph quadrant is one of four sections on a Cartesian plane. Each of the four sections has a specific combination of negative and positive values for x and y. We plot an ordered pair on graph quadrants. Ordered pairs have x and y values. X is the first value in an ordered pair; y is the second, the x value refers to the pair’s horizontal position on the graph. The y value refers to the vertical position.