Question

Quadrant of -9, 17? I cannot find the answer to the question

Answer 1

it’s in the second quadrant

Answer 2

`(-9,\, 17)` is in the second quadrant of a cartesian plane.

Explanation:

The horizontal and vertical axes divides the cartesian plane into four quadrants. The quadrants are numbered counterclockwise, starting from the top-right corner:

`\begin{array}c\text{second quadrant} & \text{first quadrant} \\\cline{1-2} \text{third quadrant} & \text{fourth quadrant}\end{array}`.

(The quadrants do not include the two axes. Points on either axes are not in any of the quadrant.)

A point in the form
`(x_(0),\, y_(0))` is on the right half of the plane (to the right of the vertical axis) if
`x_(0) > 0`. This point is on the vertical axis through the middle of the plane if
`x_(0) = 0`. Otherwise, if
`x_(0) < 0`, this point would be on the left half of the plane (to the left of the vertical axis.)

The
`x`-coordinate of
`(-9,\, 17)` is
`x_(0) = -9`.

Since the
`x`-coordinate of this point is below zero (
`(-9) < 0`), this point would be on the left-hand side of the origin to the left of the vertical axis.

Likewise, a point in the form
`(x_(0),\, y_(0))` is above the horizontal axis if
`y_(0) > 0`, on the horizontal axis if
`y_(0) = 0`, and below the horizontal axis if
`y_(0) < 0`.

The
`y`-coordinate of the given point
`(-9,\, 17)` in this question is
`y_(0) = 17`.

Since the
`y`-coordinate of this point is greater than zero (
`17 > 0`), this point would be above the horizontal axis.

Thus, the point
`(-9,\, 17)` would be in the top-left quarter of the plane. The top-left quarter of the plane corresponds to the second quadrant, since this quadrant is the second quadrant after the first quadrant in the top-right corner. Hence,
`(-9,\, 17)\!` would be in the second quadrant of the plane.