Respuesta :
Answer:
[tex](-9,\, 17)[/tex] is in the second quadrant of a cartesian plane.
Step-by-step explanation:
The horizontal and vertical axes divides the cartesian plane into four quadrants. The quadrants are numbered counterclockwise, starting from the top-right corner:
[tex]\begin{array}{c|c}\text{second quadrant} & \text{first quadrant} \\\cline{1-2} \text{third quadrant} & \text{fourth quadrant}\end{array}[/tex].
(The quadrants do not include the two axes. Points on either axes are not in any of the quadrant.)
A point in the form [tex](x_{0},\, y_{0})[/tex] is on the right half of the plane (to the right of the vertical axis) if [tex]x_{0} > 0[/tex]. This point is on the vertical axis through the middle of the plane if [tex]x_{0} = 0[/tex]. Otherwise, if [tex]x_{0} < 0[/tex], this point would be on the left half of the plane (to the left of the vertical axis.)
The [tex]x[/tex]-coordinate of [tex](-9,\, 17)[/tex] is [tex]x_{0} = -9[/tex].
Since the [tex]x[/tex]-coordinate of this point is below zero ([tex](-9) < 0[/tex]), 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 [tex](x_{0},\, y_{0})[/tex] is above the horizontal axis if [tex]y_{0} > 0[/tex], on the horizontal axis if [tex]y_{0} = 0[/tex], and below the horizontal axis if [tex]y_{0} < 0[/tex].
The [tex]y[/tex]-coordinate of the given point [tex](-9,\, 17)[/tex] in this question is [tex]y_{0} = 17[/tex].
Since the [tex]y[/tex]-coordinate of this point is greater than zero ([tex]17 > 0[/tex]), this point would be above the horizontal axis.
Thus, the point [tex](-9,\, 17)[/tex] 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, [tex](-9,\, 17)\![/tex] would be in the second quadrant of the plane.
