Question

lesson summary

• the x - axis and y - axis of the coordinate plane are number lines that intersect at zero on each number line.
• the axes partition the coordinate plane into four quadrants.
• points in the coordinate plane lie either on an axis or in one of the four quadrants.

problem set
1 name the quadrant in which each of the points lies. if the point does not lie in a quadrant, specify which axis the point lies on.
a (-2,5)
b (0,-4)
c (-1,-8)
d (9.2,7)
e (0,-4)
2 jackie claims that points with the same x - and y - coordinates must lie in quadrant i or quadrant iii. do you agree or disagree? explain your answer.
3 locate and label each set of points on the coordinate plane. describe similarities of the ordered pairs in each set, and describe the points on the plane.
a {(-2,5),(-2,2),(-2,7),(-2,-3),(-2,-0.8)}
b {(-9,9),(-4,4),(-2,2),(1,-1),(3,-3),(0,0)}
c {(-7,-8),(5,-8),(0,-8),(10,-8),(-3,-8)}

Explanation:

Step1: Recall quadrant rules

In a coordinate - plane, if \(x<0,y > 0\), point is in Quadrant II; if \(x = 0\), point is on \(y\) - axis; if \(x<0,y<0\), point is in Quadrant III; if \(x>0,y>0\), point is in Quadrant I.

Step2: Analyze point a (-2,5)

Since \(x=-2<0\) and \(y = 5>0\), it is in Quadrant II.

Step3: Analyze point b (0, - 4)

Since \(x = 0\), it is on the \(y\) - axis.

Step4: Analyze point c (-1,-8)

Since \(x=-1<0\) and \(y=-8<0\), it is in Quadrant III.

Step5: Analyze point d (9.2,7)

Since \(x = 9.2>0\) and \(y = 7>0\), it is in Quadrant I.

Step6: Analyze point e (0,-4)

Since \(x = 0\), it is on the \(y\) - axis.

Answer:

a. Quadrant II
b. \(y\) - axis
c. Quadrant III
d. Quadrant I
e. \(y\) - axis