Question

Write the quadrants where the following points will lie. (a) (-20,13), (b) (-12, -8 ).​

Answer 1

Answer:

$(-20,\, 13)$ would be in the second quadrant of the cartesian plane.

$(-12,\, -8)$ would be in the third quadrant of the cartesian plane.

Step-by-step explanation:

The horizontal and vertical axes of the cartesian plane divides the plane into four quadrants. By convention, these quadrants are numbered counterclockwise starting from the quadrant on the top right:

$\begin{array}{c|c}\text{Second Quadrant} & \text{First Quadrant} \\ \cline{1-2}\\[-1em] \text{Third Quadrant} & \text{Fourth Quadrant}\end{array}$.

• Top-left: first quadrant.
• Top-right: second quadrant.
• Bottom-left: third quadrant.
• Bottom-right: fourth quadrant.
• Points on either axes (where at least one of the coordinates is $0$) are not in any of the four quadrants.

The $x$-coordinate of the first point, $(-20,\, 13)$, is $x = -20$, which is negative. Thus, this point would be to the left of the vertical axis.

Since the $y$-coordinate of this point, $y = 13$, is positive, this point would be above the horizontal axis.

Thus, the point $(-20,\, 13)$ would be in the quadrant on the top-left corner of the cartesian plane. Therefore, this point would be in the second quadrant of the plane.

The second point $(-12,\, -8)$ would also be to the left of the vertical axis since the $x$-coordinate of this point, $x = -12$, is negative.

This point would be below the horizontal axis since the $y$-coordinate of this point $y = -8$ is negative.

Thus, the point $(-12,\, -8)$ would be in the quadrant on the lower-left corner of the cartesian plane. This point would be thus be in the third quadrant of the plane.