Question

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

Answer 1

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

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

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\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.