Question

for the point shown in the xy-plane, write the corresponding ordered pair and name the quadrant in which it lies or the axis on which it lies. the ordered pair associated with the given point is (-1, -6). (type an ordered pair.) where does the point lie? (\bigcirc) a. quadrant i (\bigcirc) b. quadrant ii (\bigcirc) c. quadrant iv (\bigcirc) d. quadrant iii (\bigcirc) e. y-axis (\bigcirc) f. x-axis

Explanation:

Step1: Recall quadrant rules

In the xy - plane, Quadrant I has \(x>0,y > 0\), Quadrant II has \(x<0,y>0\), Quadrant III has \(x < 0,y<0\), Quadrant IV has \(x>0,y < 0\). Points on the x - axis have \(y = 0\), points on the y - axis have \(x=0\).

Step2: Analyze the ordered pair \((-1,-6)\)

For the point \((-1,-6)\), the x - coordinate \(x=-1<0\) and the y - coordinate \(y = - 6<0\). By the quadrant rules, when both \(x\) and \(y\) are negative, the point lies in Quadrant III.

Answer:

D. Quadrant III